RR Fluxes Research Articles

Comments on integrability in the symmetric orbifold

We present a map between the excitation of the symmetric-product orbifold CFT of T4, and of the worldsheet-integrability description of AdS3 × S3 × T4 of Lloyd, Ohlsson Sax, Sfondrini, and Stefański at k = 1. We discuss the map in the absence of RR fluxes, when the theory is free, and at small RR flux, h ≪ 1, where the symmetric-orbifold CFT is deformed by a marginal operator from the twist-two sector. We discuss the recent results of Gaberdiel, Gopakumar, and Nairz, who computed from the perturbed symmetric-product orbifold the central extension to the symmetry algebra of the theory and its coproduct. We show that it coincides with the h ≪ 1 expansion of the lightcone symmetry algebra known from worldsheet integrability, and that hence the S matrix found by Gaberdiel, Gopakumar, and Nairz maps to the one bootstrapped by the worldsheet integrability approach.

Exploring the Quantum Spectral Curve for AdS3/CFT2

Despite the rich and fruitful history of the integrability approach to string theory on the AdS3 × S3 × T4 background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. In other integrable superstring backgrounds there is compelling evidence that this formulation captures all wrapping effects exactly and describes the full planar spectrum. This great success motivates us to study the new proposed QSC and develop methods to extract from it concrete predictions for spectral data. The AdS3 × S3 × T4 case presents a significant novel feature and challenge compared to its higher-dimensional analogues — massless modes. It has been conjectured that these manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for unprotected string excitations in the planar limit with finite quantum numbers and RR flux. We explain how to extract a systematic expansion around the analogue of the weak ’t Hooft coupling limit in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM and also obtain high-precision numerical results. These concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.

The black hole/string transition in AdS3 and confining backgrounds

String stars, or Horowitz-Polchinski solutions, are Euclidean string theory saddles with a normalizable condensate of thermal winding strings. String stars were suggested as a possible description of stringy (Euclidean) black holes close to the Hagedorn temperature. In this work, we continue the study initiated in [1] by investigating the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter backgrounds. First, we discuss the case of AdS3 with mixed RR and NS-NS fluxes (including the pure NS-NS system) and comment on a possible BTZ/string transition unique to AdS3. Second, we present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model and determine the subleading correction to their Hagedorn temperature. We speculate a black brane/string transition in these models and argue for a possible relation to the deconfined phase of 3+1 dimensional pure Yang-Mills.

Generalised U-dual solutions via ISO(7) gauged supergravity

We study a solution generating technique in supergravity which can be viewed as a generalised version of U-duality, taking solutions of type IIA supergravity on a 6-sphere with RR flux to new solutions of 11-dimensional supergravity. The new solutions are characterised by an underlying 6-algebra structure. Our construction provides an 11-dimensional uplift of four-dimensional ISO(7) gauged supergravity, using E7 exceptional geometry techniques. We focus on an example where we start with the D2 solution in type IIA supergravity and construct a new frac{1}{2} -BPS 11-dimensional solution.

Integrable supersymmetric deformations of AdS3× S3× T4

We construct a family of type IIB string backgrounds that are deformations of AdS3× S3× T4 with a “squashed” AdS3× S3 metric supported by a combination of NSNS and RR fluxes. They have global SU(1, 1) × SU(2) symmetry, regular curvature, constant dilaton and preserve 8 supercharges. Upon compactification to 4 dimensions they reduce to mathcal{N} = 2 supersymmetric AdS2× S2 solutions with electric and magnetic Maxwell fluxes. These type IIB supergravity solutions can be found from the undeformed AdS3× S3× T4 background by a combination of T-dualities and S-duality. In contrast to T-duality, S-duality transformations of a type IIB supergravity background do not generally preserve the classical integrability of the corresponding Green-Schwarz superstring sigma model. Nevertheless, we show that integrability is preserved in the present case. Indeed, we find that these backgrounds can be obtained, up to T-dualities, from an integrable inhomogeneous Yang-Baxter deformation (with unimodular Drinfel’d-Jimbo R-matrix) of the original AdS3× S3 supercoset model.

On type 0 string theory in solvable RR backgrounds

Motivated by a possibility of solving non-supersymmetric type 0 string theory in AdS5× S5 background using integrability, we revisit the construction of type 0 string spectrum in some solvable examples of backgrounds with RR fluxes that are common to type IIB and type 0B theories. The presence of RR fluxes requires the use of a Green-Schwarz description for type 0 string theory. Like in flat space, the spectrum of type 0 theory can be derived from the type II theory spectrum by a (−1)F orbifolding, i.e. combining the untwisted sector where GS fermions are periodic with the twisted sector where GS fermions are antiperiodic (and projecting out all spacetime fermionic states). This construction of the type 0 spectrum may also be implemented using Melvin background that allows to continuously interpolate between the type II and type 0 theories. As an illustration, we discuss the type 0B spectrum in the pp-wave background which is the Penrose limit of AdS5× S5 with RR 5-form flux and also in the pp-wave background which is the Penrose limit of AdS3× S3× T4 supported by mixed RR and NSNS 3-form fluxes. We show that increasing the strength of the RR flux increases the value of the effective normal ordering constant (which determines the mass of the type 0 tachyon in flat space) and thus effectively decreases the momentum-space domain of instability of the ground state. We also comment on the semiclassical sector of states of type 0B theory in AdS5× S5.

Two particle spectrum of tensor multiplets coupled to AdS3×S3 gravity

We study certain infinite families of two-particle operators exchanged in 4pt correlators $⟨{\mathcal{O}}_{{p}_{1}}{\mathcal{O}}_{{p}_{2}}{\mathcal{O}}_{{p}_{3}}{\mathcal{O}}_{{p}_{4}}⟩$ of tensor multiplets living on the ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}$ background. This is the weakly curved, weakly coupled SUGRA theory dual to the D1-D5 system with RR flux. At tree level in Mellin space, all these correlators are nicely determined by a single amplitude, which makes manifest the large $p$ limit, the connection with the flat space S-matrix, and a six dimensional conformal symmetry. We compute the $(1,1)\ifmmode\times\else\texttimes\fi{}\overline{(1,1)}$ superconformal blocks for the two-dimensional $\mathcal{N}=(4,4)$ conformal theory at the boundary, and then we obtain a formula for the anomalous dimensions of the two-particle operators exchanged in the symmetric and antisymmetric flavor channels. These anomalous dimensions solve a mixing problem which is analogous to the one in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ with interesting modifications. Along the way we show how the $(1,1)\ifmmode\times\else\texttimes\fi{}\overline{(1,1)}$ superconformal blocks relate to those in $\mathcal{N}=4$ SYM in four dimensions, and provide new intuition on the known data for ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$.

On supersymmetric AdS3 solutions of Type II

We classify supersymmetric warped AdS3×wM7 backgrounds of Type IIA and Type IIB supergravity with non-constant dilaton, generic RR fluxes and magnetic NSNS flux, in terms of a dynamic SU(3)-structure on M7. We illustrate our results by recovering several solutions with various amounts of supersymmetry. The dynamic SU(3)-structure includes a G2-structure as a limiting case, and we show that in Type IIB this is integrable.

AdS2 \xd7 S2 \xd7 CY2 solutions in Type IIB with 8 supersymmetries

We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

Strings in Ramond-Ramond backgrounds from the Neveu-Schwarz-Ramond formalism

We treat RR flux backgrounds of type II string theory in the framework of closed superstring field theory based on the NSR formalism, focusing on two examples: (1) the pp-wave background supported by 5-form flux, and (2) AdS3 × S3 × M4 supported by mixed 3-form fluxes. In both cases, we analyze the classical string field solution perturbatively, and compute the correction to the dispersion relation of string states to quadratic order in the RR flux. In the first example, our result is in a delicate way consistent with that obtained from lightcone quantization of the Green-Schwarz string. In the second example, we will obtain numerically the mass corrections to pulsating type IIB strings in AdS3 × S3 × M4. Our results, valid at finite AdS radius, agree with previously known answers in the semiclassical limit and in the BMN limit respectively.

Higher form symmetries of Argyres-Douglas theories

We determine the structure of 1-form symmetries for all 4d mathcal{N} = 2 theories that have a geometric engineering in terms of type IIB string theory on isolated hypersurface singularities. This is a large class of models, that includes Argyres-Douglas theories and many others. Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1-form symmetries can be obtained via a careful analysis of the non-commutative behaviour of RR fluxes at infinity in the IIB setup. The final result admits a very compact field theoretical reformulation in terms of the BPS quiver. We illustrate our methods in detail in the case of the ( mathfrak{g},{mathfrak{g}}^{prime } ) Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where mathcal{N} = 1 gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such mathcal{N} = 1 Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals.

N spike D-strings in AdS Space with mixed flux

We use Dirac-Born-Infeld action to study the spinning D-string in AdS_3 background in the presence of both NS-NS and RR fluxes. We compute the scaling relation between the energy (E) and spin (S) in the ‘long string limit’. The energy of these spiky string is found to be a function of spin with the leading logarithmic behaviour and the scaling relation appears to be independent of the amount of flux present. We further discuss folded D-string solutions in AdS_3 background with pure NS-NS and R-R fluxes.

Gaugino mass term for D-branes and Generalized Complex Geometry

We compute the four-dimensional gaugino mass for a Dp-brane extended in spacetime and wrapping a cycle on the internal geometry in a warped compactification with fluxes. Motivated by the backreaction of gaugino bilinear VEVs, we use Generalized Complex Geometry to characterize the internal geometry as well as the cycle wrapped by the brane. We find that the RR fluxes and the non-closure of the generalized complex structures combine in the gaugino mass terms in the same form as they do in the bulk superpotential, while for the NSNS fluxes there is a crucial minus sign in the component normal to the brane. Our expression extends the known result for D3 and D7-branes in Calabi-Yau manifolds, where the gaugino masses are induced respectively by the imaginary anti-self dual and imaginary self-dual components of the complex 3-form flux G3.

IIB flux non-commutativity and the global structure of field theories

We discuss the origin of the choice of global structure for six dimensional (2, 0) theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of mathcal{N} = 4 theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of mathcal{N} = 4 ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional (1, 0) theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects.

On N-spike strings in conformal gauge with NS-NS fluxes

The AdS3 × S3 string sigma model supported both by NS-NS and R-R fluxes has become a well known integrable model, however a putative dual field theory description remains incomplete. We study the anomalous dimensions of twist operators in this theory via semiclassical string methods. We describe the construction of a multi-cusp closed string in conformal gauge moving in AdS3 with fluxes, which supposedly is dual to a general higher twist operator. After analyzing the string profiles and conserved charges for the string, we find the exact dispersion relation between the charges in the ‘long’ string limit. This dispersion relation in leading order turns out to be similar to the case of pure RR flux, with the coupling being scaled by a factor that depends on the amount of NS-NS flux turned on. We also analyse the case of pure NS flux, where the dispersion relation simplifies considerably. Furthermore, we discuss the implications of these results at length.

Type IIA flux vacua and \u03b1\u2032-corrections

We analyse type IIA Calabi-Yau orientifolds with background fluxes, taking into account the effect of perturbative α′-corrections. In particular, we consider the α′ corrections that modify the metrics in the Kähler sector of the compactification. As it has been argued in the literature, including such α′-corrections allows to construct the mirror duals of type IIB Calabi-Yau flux compactifications, in which the effect of flux backreaction is under control. We compute the α′-corrected scalar potential generated by the presence of RR and NS fluxes, and reformulate it as a bilinear of the flux-axion polynomials invariant under the discrete shift symmetries of the compactification. The use of such invariants allows to express in a compact and simple manner the conditions for Minkowski and AdS flux vacua, and to extract the effect of α′-corrections on them.

Poisson-Lie duals of the \u03b7-deformed AdS2 \xd7 S2 \xd7 T6 superstring

We investigate Poisson-Lie duals of the η-deformed AdS2 ×S2 ×T6 superstring. The η-deformed background satisfies a generalisation of the type II supergravity equations. We discuss three Poisson-Lie duals, with respect to (i) the full mathfrak{p}mathfrak{s}mathfrak{u}left(1,left.1right|2right) superalgebra, (ii) the full bosonic subalgebra and (iii) the Cartan subalgebra, for which the corresponding backgrounds are expected to satisfy the standard type II supergravity equations. The metrics and B-fields for the first two cases are the same and given by an analytic continuation of the λ-deformed model on AdS2 × S2 × T6 with the torus undeformed. However, the RR fluxes and dilaton will differ. Focusing on the second case we explicitly derive the background and show agreement with an analytic continuation of a known embedding of the λ-deformed model on AdS2 × S2 in type II supergravity.

On pp wave limit for \u03b7 deformed superstrings

In this paper, based on the notion of plane wave string/gauge theory duality, we explore the pp wave limit associated with the bosonic sector of η deformed superstrings propagating in (AdS5 × S5)η . Our analysis reveals that in the presence of NS-NS and RR fluxes, the pp wave limit associated to full ABF background satisfies type IIB equations in its standard form. However, the beta functions as well as the string Hamiltonian start receiving non trivial curvature corrections as one starts probing beyond pp wave limit which thereby takes solutions away from the standard type IIB form. Furthermore, using uniform gauge, we also explore the BMN dynamics associated with short strings and compute the corresponding Hamiltonian density. Finally, we explore the Penrose limit associated with the HT background and compute the corresponding stringy spectrum for the bosonic sector.

Closed strings and moduli in AdS3/CFT2

String theory on AdS3 × S3 × T4 has 20 moduli. We investigate how the perturbative closed string spectrum changes as we move around this moduli space in both the RR and NSNS flux backgrounds. We find that, at weak string coupling, only four of the moduli affect the energies. In the RR background the only effect of these moduli is to change the radius of curvature of the background. On the other hand, in the NSNS background, the moduli introduce worldsheet interactions which enable the use of integrability methods to solve the spectral problem. Our results show that the worldsheet theory is integrable across the 20 dimensional moduli space.

Three-forms in supergravity and flux compactifications

We present a duality procedure that relates conventional four-dimensional matter-coupled mathcal{N}=1 supergravities to dual formulations in which auxiliary fields are replaced by field strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the superpotential to vacuum expectation values of the field strengths. We then apply this general duality to type IIA string compactifications on Calabi–Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms.