Fractional D3-branes Research Articles

Chiral magnets from string theory

Chiral magnets with the Dzyaloshinskii-Moriya (DM) interaction have received quite an intensive focus in condensed matter physics because of the presence of a chiral soliton lattice (CSL), an array of magnetic domain walls and anti-domain walls, and magnetic skyrmions, both of which are important ingredients in the current nanotechnology. In this paper, we realize chiral magnets in type-IIA/B string theory by using the Hanany-Witten brane configuration (consisting of D3, D5 and NS5-branes) and the fractional D2 and D6 branes on the Eguchi-Hanson manifold. In the both cases, we put constant non-Abelian magnetic fluxes on higher dimensional (flavor) D-branes, turning them into magnetized D-branes. The O(3) sigma model with an easy-axis or easy-plane potential and the DM interaction is realized on the worldvolume of the lower dimensional (color) D-branes. The ground state is the ferromagnetic (uniform) phase and the color D-brane is straight when the DM interaction is small compared with the scalar mass. However, when the DM interaction is larger, the uniform state is no longer stable and the ground state is inhomogeneous: the CSL phases and helimagnetic phase. In this case, the color D-brane is no longer straight but is snaky (zigzag) when the DM interaction is smaller (larger) than a critical value. A magnetic domain wall in the ferromagnetic phase is realized as a kinky D-brane. We further construct magnetic skyrmions in the ferromagnetic phase, realized as D1-branes (fractional D0-branes) in the former (latter) configuration. We see that the host D2-brane is bent around the position of a D0-brane as a magnetic skyrmion. Finally, we construct, in the ferromagnetic phase, domain-wall skyrmions, that is, composite states of a domain wall and skyrmions, and find that the domain wall is no longer flat in the vicinity of the skyrmion. Consequently, a kinky D2-brane worldvolume is pulled or pushed in the vicinity of the D0-brane depending on the sign of the skyrmion topological charge.

Surface defects from fractional branes. Part II

A generic half-BPS surface defect of mathcal{N} = 4 supersymmetric U(N ) Yang- Mills theory is described by a partition of N = n1 + . . . + nM and a set of 4M continuous parameters. We show that such a defect can be realized by nI stacks of fractional D3-branes in Type II B string theory on a ℤM orbifold background in which the brane world-volume is partially extended along the orbifold directions. In this set up we show that the 4M continuous parameters correspond to constant background values of certain twisted closed string scalars of the orbifold. These results extend and generalize what we have presented for the simple defects in a previous paper.

Surface defects from fractional branes. Part I

We show that the Gukov-Witten monodromy defects of supersymmetric Yang-Mills theory can be realized in perturbative string theory by considering an orbifold background of the Kanno-Tachikawa type and placing stacks of fractional D3-branes whose world-volume partially extends along the orbifold directions. In particular, we show that turning on a constant background value for some scalar fields in the closed string twisted sectors induces a non-trivial profile for the gauge field and one of the complex scalars of the world-volume theory, and that this profile exactly matches the singular behavior that one expects for a Gukov-Witten surface defect in the mathcal{N} = 4 super Yang-Mills theory. To keep the presentation as simple as possible, in this work we restrict our analysis to surface defects corresponding to a ℤ2 orbifold and defer the study of the most general case to a companion paper.

Supersymmetry breaking warped throats and the weak gravity conjecture

We generalize the swampland criterion forbidding stable non-supersymmetric AdS vacua and propose a new swampland conjecture forbidding stable non-supersymmetric “locally AdS” warped throats. The conjecture is motivated by the properties of systems of fractional D3-branes at singularities, and can be used to rule out large classes of warped throats with supersymmetry breaking ingredients, and their possible application to de Sitter uplift. In particular, this allows to reinterpret the runaway instabilities of the gravity dual of fractional branes in the dP1 theory, and to rule out warped throats with Dynamical Supersymmetry Breaking D-brane sectors at their bottom. We also discuss the instabilities of warped throats with supersymmetry broken by the introduction of anti-orientifold planes. These examples lead to novel decay mechanisms in explicit non-supersymmetric examples of locally AdS warped throats, and also of pure AdS backgrounds.

Non-BPS fractional branes with Bose-Fermi cancellation in asymmetric orbifolds

We study non-BPS D-branes in the type II string vacua with chiral space-time SUSY constructed based on the asymmetric orbifolds of mathrm{K}3cong {T}^4/{mathrm{mathbb{Z}}}_2 as a succeeding work of [21]. We especially focus on the fractional D-branes that contains the contributions from the twisted sector of the {mathrm{mathbb{Z}}}_2 -orbifolding.We show that the cylinder partition functions for these fractional branes do not vanish, as in the cases of ordinary non-BPS D-branes. This aspect is in a sharp contrast with the bulk-type branes studied in [21]. We then discuss the extensions of models by including the discrete torsion depending on the spin structures, and investigate whether we obtain the vanishing self-overlaps associated to the fractional branes. The existence/absence of bose-fermi cancellations both in the closed and open string spectra as well as the massless spectra in the twisted sectors crucially depend on the discrete torsion. We find that some choices of the torsion indeed realize the vanishing self-overlaps for the fractional branes, with keeping the vanishing torus partition function intact.

Massless spectra and gauge couplings at one-loop on non-factorisable toroidal orientifolds

So-called ‘non-factorisable’ toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al. [1] provides a new avenue to Conformal Field Theory methods, by which the vector-like massless matter spectrum – and thereby the type of gauge group enhancement on orientifold invariant fractional D6-branes – and the one-loop corrections to the gauge couplings in Type IIA orientifold theories can be computed in addition to the well-established chiral matter spectrum derived from topological intersection numbers among three-cycles. We demonstrate this framework for the Z4×ΩR orientifolds on the A3×A1×B2-type torus. As observed before for factorisable backgrounds, also here the one-loop correction can drive the gauge groups to stronger coupling as demonstrated by means of a four-generation Pati–Salam example.

Global orientifolded quivers with inflation

We describe global embeddings of fractional D3 branes at orientifolded singularities in type IIB flux compactifications. We present an explicit Calabi-Yau example where the chiral visible sector lives on a local orientifolded quiver while non-perturbative effects, α′ corrections and a T-brane hidden sector lead to full closed string moduli stabilisation in a de Sitter vacuum. The same model can also successfully give rise to inflation driven by a del Pezzo divisor. Our model represents the first explicit Calabi-Yau example featuring both an inflationary and a chiral visible sector.

On D-brane dynamics and moduli stabilization

We discuss the effect of the dynamics of D-branes on moduli stabilization in type IIB string theory compactifications, with reference to a concrete toy model of [Formula: see text] orientifold compactification with fractional D3-branes and anti-D3-branes at orbifold fixed points. The resulting attractive forces between anti-D3-branes and D3-branes, together with the repulsive forces between anti-D3-branes and O3-planes, can affect the stability of the compact space. There are no complex structure moduli in [Formula: see text] orientifold, which should thus capture some generic features of more general settings where all complex structure moduli are stabilized by three-form fluxes. The simultaneous presence of branes and anti-branes brings along the breaking of supersymmetry. Non-BPS combinations of this type are typical of “brane supersymmetry breaking” and are a necessary ingredient in the KKLT scenario for stabilizing the remaining Kähler moduli. The conclusion of our analysis is that, while mutual D-brane interactions sometimes help Kähler moduli stabilization, this is not always the case.

Testing 5d-6d dualities with fractional D-branes

6d SCFTs compactified on a circle can often be studied from nonperturbative 5d super-Yang-Mills theories, using instanton solitons. However, the 5d Yang-Mills theories with 6d UV fixed points frequently have too many hypermultiplet matters, which makes it difficult to use the ADHM techniques for instantons. With the examples of 6d $\mathcal{N}=(1,0)$ SCFTs with $Sp(N)$ gauge symmetry and $2N+8$ fundamental hypermultiplets, we show that one can still make rigorous studies of these 5d-6d relations in the `fractional D-brane sectors'. We test the recently proposed 5d duals given by $Sp(N+1)$ gauge theories, and compare their instanton partition functions with the elliptic genera of 6d self-dual strings.

New insights into properties of large-N holographic thermal QCD at finite gauge coupling at (the non-conformal/next-to) leading order in N

It is believed that large-N thermal QCD laboratories like strongly coupled QGP (sQGP) require not only a large ‘t Hooft coupling but also a finite gauge coupling (Natsuume, String theory and quark–gluon plasma. arXiv:hep-ph/0701201 , 2007). Unlike almost all top–down holographic models in the literature, holographic large-N thermal QCD models, based on this assumption, therefore necessarily require addressing this limit from M-theory. This was initiated in Dhuria and Misra (JHEP 1311:001, 2013) which presented a local M-theory uplift of the string theoretic dual of large-N thermal QCD-like theories at finite gauge/string coupling of Mia et al. (Nucl. Phys. B 839:187, arXiv:0902.1540 [hep-th], 2010) ( $$g_s\mathop {<}\limits ^{\sim }1$$ as part of the ‘MQGP’ limit of Dhuria and Misra in JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013). Understanding and classifying the properties of systems like sQGP from a top–down holographic model, assuming a finite gauge coupling, have been entirely missing in the literature. In this paper we largely address the following two non-trivial issues pertaining to the same. First, up to LO in N (the number of D3-branes), by calculating the temperature dependence of the thermal (and electrical) conductivity and the consequent deviation from the Wiedemann–Franz law, upon comparison with Garg et al. (Phys. Rev. Lett. 103:096402, 2009), we show that, remarkably, the results qualitatively mimic a 1+1-dimensional Luttinger liquid with impurities. Second, by looking at, respectively, the scalar, vector, and tensor modes of metric perturbations and using the prescription of Kovtun and Starinets (Phys. Rev. D 72:086009, arXiv:hep-th/0506184 , 2005) for constructing appropriate gauge-invariant perturbations, we obtain the non-conformal corrections to the conformal results (but at finite $$g_s$$ ), respectively, for the speed of sound, the shear mode diffusion constant, and the shear viscosity $$\eta $$ (and $$\frac{\eta }{s}$$ ). The new insight gained is that it turns out that these corrections show a partial universality in the sense that at NLO in N the same are given by the product of $$\frac{(g_s M^2)}{N}\ll 1$$ and $$g_s N_f\sim \mathcal{O}(1)$$ , $$N_f$$ being the number of flavor D7-branes and M the number of fractional D3-branes = the number of colors = 3 in the IR after the end of a Seiberg-duality cascade. On the mathematics side, using the results of Ionel and Min-OO (Ill. J. Math. 52, 2008), at LO in N we finish our argument of Dhuria and Misra (Eur. Phys. J. C 75:16, 2015) and show that for a predominantly resolved (resolution > deformation – this paper) or deformed (deformation > resolution – Dhuria and Misra in Eur Phys J C 75(1):16, arXiv:1406.6076 [hep-th], 2015) resolved warped deformed conifold, the local $$T^3$$ of Dhuria and Misra (JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013) in the MQGP limit is the $$T^2$$ -invariant special Lagrangian three-cycle of Ionel and Min-OO (Ill J Math 52(3), 2008) justifying the construction in Dhuria and Misra (JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013) of the delocalized Strominger–Yau–Zaslow Type IIA mirror of the Type IIB background of Mia et al. (Nucl Phys B 839:187, arXiv:0902.1540 [hep-th], 2010).

Non-abelian T-dualizing the resolved conifold with regular and fractional D3-branes

In this paper we obtain new solutions of Type IIA and massive Type IIA supergravity. These solutions are the result of implementing a non-abelian T-duality along the internal $SU(2)$ isometries of several D3-brane configurations on the resolved conifold, studied by Pando Zayas and Tseytlin. We first study the pure NS resolved conifold solution, then we add fluxes by placing a stack of D3-branes at the tip of the resolved conifold and finally we consider the system of regular and fractional D3-branes at the tip. We present the non-abelian T-duals associated with these backgrounds and study their geometries and fluxes. We briefly comment on some field theory features by studying couplings and the central charge of the dual field theory. We also analyze the supersymmetry of the dual solutions and show that for the system of only D3 branes the duality defines a map between backgrounds with $SU(3)$ and orthogonal $SU(2)$ structures.

Transport coefficients of black MQGP $$M3$$ M 3 -branes

The SYZ mirror, in the `delocalized limit' of [1], of (M)N (fractional)D3-branes, and wrapped N_f flavor D7-branes in the presence of a black-hole resulting in a non-Kaehler resolved warped deformed conifold (NKRWDC) in [2], was carried out in [3] and resulted in black M3-branes. The uplift, if valid globally(like [4] for fractional D3 branes in conifolds), asymptotes to M5-branes wrapping a two-cycle (homologously an (large) integer sum of two-spheres) in AdS_5xM_6. Interestingly, in the MQGP limit, assuming the deformation > resolution, by estimating the five SU(3) structure torsion (\tau) classes W_{1,2,3,4,5} we show that \tau\in W_4+W_5: 2/3 Re(W^3bar_5)=W^3bar_4 in the UV, implying the NKRWDC locally preserves SUSY. Further, the local T^3 of [3] in the large-r limit and the `MQGP' limit of [3], satisfies the same conditions as the maximal T^2-invariant special Lagrangian three-cycle of T^*(S^3) of [6], partly justifying use of local SYZ mirror symmetry in [3]. Using the Ouyang embedding in the DBI action of a D7-brane or by dimensionally reducing the 11-dimensional EH action to five (R^{1,3},r) dimensions, we then calculate a variety of gauge and metric-perturbation-modes' two-point functions using the prescription of [5], and show: (i) diffusion constant D~1/T, (ii) the electrical conductivity \sigma~T, (iii) the charge susceptibility \chi~ T^2, (iv) [using (i) - (iii)] the Einstein's relation \sigma/\chi=D, is indeed satisfied, (v) the R-charge diffusion constant D_R~1/T, and (vi) the possibility of generating \eta/s=1/4pi from solutions to the vector and tensor mode metric perturbations' EOMs, separately. All results are also valid in the limit of [2].

Circling the square: deforming fractional D-branes in type II/Ω ℛ $$ \mathrm{\mathcal{R}} $$ orientifolds

We study complex structure deformations of special Lagrangian cycles associated to fractional D-branes at $\mathbb{Z}_2$ singularities in Type II/$\Omega \mathcal{R}$ orientifold models. By means of solving hypersurface constraints, we show how to compute the volumes of the most simple D-brane configurations. These volumes are given as a function of the deformation parameters depending on the D-brane position relative to the smoothed out singularity. We observe which cycles keep the special Lagrangian property in various deformation scenarios and what orientifold involutions are allowed. As expected, the volume and thus the tree level value of the gauge coupling hardly change for D-branes not wrapping the exceptional cycle on the deformed singularity, whereas the volume of D-branes passing through the singularity depends on the deformation parameter by some power law.

A novel cross-check of localization and non conformal holography

We precisely reproduce the perimeter law obeyed by Wilson loops on large spatial contours in planar N=2 SYM at strong coupling, as recently deduced using localization, by means of a dual holographic model. The relevant supergravity background is sourced by D5-branes wrapped on a two-sphere in a Calabi-Yau two-manifold. Thus, localization and holography are cross-checked, for the first time, in a non conformal context where the gravity background is not asymptotically Anti de Sitter and the dual gauge theory has a logarithmically running coupling. We also notice that the same cross-check can be performed considering an alternative holographic description of N=2 SYM based on a background sourced by fractional D3-branes.

Towards MQGP

Using the type IIB background of [1] — a gravity dual to a large-N thermal QCD-like theory in the presence of N f thermal quarks — we calculate the chemical potential μ C as a function of temperature due to a U(1) (cf. U(N f ) ~ SU(N f ) × U(1)) gauge field living on the world volume of N f space-time-filling D7-branes wrapped around a four-cycle in a resolved warped deformed conifold along with (M)N (fractional) D3-branes, and show that for the Ouyang embedding, $ {{\left. {\frac{{\partial {\mu_C}}}{{\partial T}}} \right|}_{{{N_f}}}}<0 $ (imlying what one expects: $ {{\left. {\frac{{\partial S}}{{\partial {N_f}}}} \right|}_T}>0 $ ) up to linear order in the embedding parameter (which we take to be real and slightly less than unity). By explicitly verifying that $ {{\left. {\frac{{\partial {\mu_C}}}{{\partial {N_f}}}} \right|}_T}>0 $ up to linear order in the embedding parameter, we demonstrate the possible thermodynamical stability of the type IIB background to that order. Analogous to [2], we then obtain a local (as the resolved warped deformed conifold does not possess a ‘third’ global killing isometry along the ‘original’ angular variable ψ ∈ [0, 4π] for implementing SYZ mirror symmetry) M-theory uplift of type IIB background by first obtaining the local type IIA mirror using SYZ mirror symmetry near $ \left( {{\theta_{1,2 }},\psi } \right)=\left( {\left\langle {{\theta_{1,2 }}} \right\rangle, \left\{ {0,2\pi, 4\pi } \right\}} \right) $ and then oxidizing the so-obtained type IIA background to M theory. We then take two limits of this uplift: (i) $ {g_s}\ll 1,{g_s}{N_f}\ll 1,\frac{{{g_s}{M^2}}}{N}\ll 1,g_s^2M{N_f}\ll 1,{g_s}M\gg 1,{g_s}N\gg 1 $ similar to [1] effected by $ M \sim {\epsilon^{{-\frac{3d }{2}}}},N\sim {\epsilon^{-19d }},{g_s}\sim {\epsilon^d},d>0 $ and $ \epsilon \leq \mathcal{O}\left( {{10^{-2 }}} \right) $ ; (ii) the second ‘MQGP limit’ $ \frac{{{g_s}{M^2}}}{N}\ll 1,{g_s}N\gg 1 $ for finite g S , M effected by: $ {g_s}\sim \epsilon, M\sim {\epsilon^{{-\frac{3d }{2}}}},N\sim {\epsilon^{-39d }},d>0,\epsilon \lesssim 1 $ . The second limit is more suited for the study of QGP (See [3]) than (i), and due to the finiteness of the string coupling can meaningfully only be addressed within an M-theoretic framework. For both limits, in this process we obtain a black M3-brane solution whose near-horizon geometry near the θ 1,2 = 0, π branches, preserves $ \frac{1}{4} $ supersymmetry. Interestingly, assuming the formula for $ \frac{\eta }{s} $ of [4] obtained for only radial-coordinate-dependent metric (i.e. μ C = 0) to also be valid for the type IIA mirror and its local M-theory up-lift having frozen the angular dependence, we obtain the value of $ \frac{\eta }{s} $ using the M theory uplift to be exactly equal to $ \frac{1}{{4\pi }} $ — there is no angular dependence in $ {G_{{tt,rr,{{\mathbf{R}}^3}}}} $ (partly justifying the assumption, further supported by the fact that the aforementioned μC can be tuned to be very small) — for both limits. In the same spirit, the diffusion constant for both, types IIB/IIA backgrounds, comes out to be the reciprocal of the temperature. The D = 11 supergravity action (Einstein-Hilbert + Gibbons-Hawking-York surface + Flux + $ \mathcal{O}\left( {\mathrm{R}4} \right) $ terms) receives the dominant contributions near $ \left\langle {{\theta_{1,2 }}} \right\rangle =0,\pi $ , where there are poles. Introducing an appropriate angular cut-off ϵ θ and using the $ \left\langle {{\theta_{1,2 }}} \right\rangle ={\epsilon_{\theta }},\pi -{\epsilon_{\theta }}\hbox{-}\mathrm{local} $ uplift the specific heat from the finite part of the action (which is found to be cut-off-independent) turns out to be positive indicative of the thermodynamical stability of the uplift. An asymptotically-linear-dilaton-gravity-type interpretation can be given to the relevant counter-terms in the limit (i). Further, it is verified that the black M3-brane entropy $ S\sim r_h^3 $ from M-theoretic thermodynamical methods as well as the horizon area calculated from the starting type IIB, mirrory type IIA and the black M3-brane solutions.

D3/D7 branes at singularities: constraints from global embedding and moduli stabilisation

In the framework of type IIB string compactifications on Calabi-Yau orientifolds we describe how to construct consistent global embeddings of models with fractional D3-branes and connected `flavour' D7-branes at del Pezzo singularities with moduli stabilisation. Our results are applied to build an explicit compact example with a left-right symmetric model at a dP_0 singularity which features three families of chiral matter and gauge coupling unification at the intermediate scale. We show how to stabilise the moduli obtaining a controlled de Sitter minimum and spontaneous supersymmetry breaking. We find an interesting non-trivial dynamical relation between the requirement of TeV-scale soft terms and the correct phenomenological values of the unified gauge coupling and unification scale.

IIA perspective on cascading gauge theory

We study the N=1 supersymmetric cascading gauge theory found in type IIB string theory on p regular and M fractional D3-branes at the tip of the conifold, using the T-dual type IIA description. We reproduce the supersymmetric vacuum structure of this theory, and show that the IIA analog of the non-supersymmetric state found by Kachru, Pearson and Verlinde in the IIB description is metastable in string theory, but the barrier for tunneling to the supersymmetric vacuum goes to infinity in the field theory limit. We also comment on the N=2 supersymmetric gauge theory corresponding to regular and fractional D3-branes on a near-singular K3, and clarify the origin of the cascade in this theory.

D-branes at del Pezzo singularities: global embedding and moduli stabilisation

In the context of type IIB string theory we combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactification. By means of toric geometry, we classify all the CY manifolds with 3 < h11 < 6 which admit two identical del Pezzo singularities mapped into each other under the orientifold involution. This effective singularity hosts the visible sector containing the Standard Model while the Kaehler moduli are stabilised via a combination of D-terms, perturbative and non-perturbative effects supported on hidden sectors. We present concrete models where the visible sector, containing the Standard Model, gauge and matter content, is built via fractional D3-branes at del Pezzo singularities and all the Kaehler moduli are fixed providing an explicit realisation of both KKLT and LARGE volume scenarios, the latter with D-term uplifting to de Sitter minima. We perform the consistency checks for global embedding such as tadpole, K-theory charges and Freed-Witten anomaly cancellation. We briefly discuss phenomenological and cosmological implications of our models.

Non-perturbative gauge/gravity correspondence in $ \mathcal{N} $ = 2 theories

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a $ {\mathbb{Z}_2} $ orbifold singularity supporting $ \mathcal{N} $ = 2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is “dual” to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.

Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on $ {T^{{6}}}/\mathbb{Z}_{{6}}^{\prime } $

The perturbative leading order open string three-point couplings for the Standard Model with hidden USp(6) on fractional D6-branes on T6/Z6' from arXiv:0806.3039 [hep-th], arXiv:0910.0843 [hep-th] are computed. Physical Yukawa couplings consisting of holomorphic Wilsonian superpotential terms times a non-holomorphic prefactor involving the corresponding classical open string Kaehler metrics are given, and mass terms for all non-chiral matter states are derived. The lepton Yukawa interactions are at leading order flavour diagonal, while the quark sector displays a more intricate pattern of mixings. While N=2 supersymmetric sectors acquire masses via only two D6-brane displacements - which also provide the hierarchies between up- and down-type Yukawas within one quark or lepton generation -, the remaining vector-like states receive masses via perturbative three-point couplings to some Standard Model singlet fields with vevs along flat directions. Couplings to the hidden sector and messengers for supersymmetry breaking are briefly discussed.