Stack Of Branes Research Articles

Hybrid inflation, reheating and dark radiation in a IIB perturbative moduli stabilization scenario

We study the cosmological implications of an effective field theory model derived within a configuration of D7 brane stacks in the framework of type-IIB string theory. We consider a suitable geometric setup where the Kähler moduli fields are stabilized and the parametric space is constrained so that a de Sitter vacuum is ensured. In addition to the moduli fields we also take into account the usual Higgs and matter fields included in the effective field theory. In this background, we implement the standard hybrid inflation scenario with a singlet scalar field acting as the inflaton and the Higgs states serving as waterfall fields. Radiative corrections and soft supersymmetry breaking terms play an essential role in the realization of a successful inflationary scenario consistent with the present cosmological data. Small tensor-to-scalar ratio values are predicted, which can be probed in future planned experiments. Further constraints on the model’s parameters are derived from bounds on dark radiation which is measured as a contribution to the effective number of neutrino species Neff. In particular, we find an excess of ∆Neff ≤ 0.95 at 2σ confidence level with natural values of the involved couplings.

Higher order corrections to KPV: The nonabelian brane stack perspective

In this work, we study the decay of D3¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D3} $$\\end{document}-branes in the setup of Kachru, Pearson, and Verlinde (KPV) at higher order in α′ from the perspective of a nonabelian D3¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D3} $$\\end{document}-brane stack. We extend the leading order analysis of KPV by including higher order commutators as well as higher derivative corrections. Recently, the KPV setup has been studied at higher order in α′ from the NS5-brane perspective. It was found that in order to control α′ corrections the quantity gsM2 determining the amount of warping in the Klebanov-Strassler throat has to be much larger than expected. This leads to serious issues when using the D3¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D3} $$\\end{document}-branes as an uplift to dS. The benefit of the analysis in this work is that the D3¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D3} $$\\end{document}-brane perspective is controlled when the distance between the branes inside the brane stack is substringy which is a regime not controlled on the NS5-brane side. As a main result, we find that the strong bound gsM2 ~ O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(100) obtained on the NS5-brane also holds in the regime accessible from the D3¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{D3} $$\\end{document}-brane perspective. We also show that the novel way of uplifting proposed in the recent work on α′ corrections to the KPV setup can only work for small warped throats.

Exact stringy microstates from gauge theories

We study how the microstates of BPS sectors in string theory are organized in the dual U(N) gauge theory. The microstates take the form of a coherent sum of stacks of branes and their open/closed string excitations. We propose a prescription to holographically construct the indices of string/brane configurations by analyzing the modifications of determinant operators in gauge theory. The string/brane configurations should be interpreted in the tensionless limit, but their indices are well-defined at finite N. In various examples, we provide evidence that a sum, of the giant graviton-type recently proposed in the literature, over all such configurations gives the finite N gauge theory index. Finally, we discuss how these microstates assemble in the BPS Hilbert space and in what circumstances the branes can form bound states to produce black hole degeneracies.

Minimal embedding of the Standard Model into intersecting D-brane configurations with a bulk leptonic U(1)

It has been recently shown that the discrepancy between the theoretical and experimental values of the anomalous magnetic moment of the muon can be fully accommodated by considering the contribution of few Kaluza–Klein (KK) states of the gauged lepton number with masses lighter than the LEP energy, consistently with present experimental limits. In this article, we construct the minimal embedding of the Standard Model (SM) into D-brane configurations with a gauged lepton number. In order to give rise to such KK modes, the lepton number gauge boson must live on an abelian U(1)_L brane extended along at least one “large” extra dimension in the bulk, with a compactification scale M_Lsim {mathcal {O}}(10{-}10^2~mathrm{GeV}) for a string scale M_sgtrsim 10~mathrm{TeV}. As a consequence, U(1)_L cannot participate to the hypercharge linear combination. We show that the minimal realisation of this framework contains five stacks of branes: the SM color U(3)_c, weak U(2)_w and abelian U(1) stacks extended effectively only in four dimensions, the bulk U(1)_L, as well as a fifth U(1)^{'} brane. With these five abelian factors, one finds besides the hypercharge a second anomaly-free linear combination which does not couple to the SM spectrum, both in the non-supersymmetric case as well as in the minimal supersymmetric extension of the model. It is also shown how the right-handed neutrino can be implemented in the spectrum, and how fermions arising from the two non-SM branes and coupled to the SM through the U(1)_L KK modes can provide Dark Matter candidates. Finally, the possibility of breaking Lepton Flavour Universality is studied by replacing U(1)_L with a brane gauging only the muonic lepton number, avoiding most experimental constraints and enlarging the parameter space for explaining the discrepancy on the muon magnetic moment.

Remarks on the Effects of Quantum Corrections on Moduli Stabilization and de Sitter Vacua in Type IIB String Theory

AbstractThe role of string loop corrections on the existence of de Sitter vacua and the moduli stabilization problem is examined in type IIB effective theories. The fundamental building blocks are a minimum of three intersecting D7 brane stacks, three Kähler moduli, and a novel Einstein‐Hilbert term associated with higher derivative terms of the 10‐dimensional effective action. It was shown in previous works that loop corrections appear which induce novel logarithmic volume‐dependent terms in the effective potential. When D‐term contributions are considered, all Kähler moduli are stabilized and de Sitter vacua are achieved. In the present work, a comprehensive study of multiple non‐perturbative terms in the superpotential is undertaken. The combined effects of the logarithmic loop corrections and two non‐perturbative superpotential Kaehler moduli dependent terms have been investigated. It is shown that a variety of fluxes exist for large as well as moderate volume compactifications which define a de Sitter space and stabilize the moduli fields. For large volumes, a generic simple form of the potential is achieved. The so obtained effective potential appears to be promising for cosmological applications.

Supersymmetry breaking, brane dynamics and Swampland conjectures

We investigate interactions between branes of various dimensions, both charged and uncharged, in three non-supersymmetric string models. These include the USp(32) and U(32) orientifold projections of the type IIB and type 0B strings, as well as the SO(16)×SO(16) projection of the exceptional heterotic string. The resulting ten-dimensional spectra are free of tachyons, and the combinations of branes that they contain give rise to rich and varied dynamics. We compute static potentials for parallel stacks of branes in three complementary regimes: the probe regime, in which one of the two stacks is parametrically heavier than the other, the string-amplitude regime, in which both stacks are light, and the holographic regime. Whenever comparisons are possible, we find qualitative agreement despite the absence of supersymmetry. For charged branes, our analysis reveals that the Weak Gravity Conjecture is satisfied in a novel way via a renormalization of the effective charge-to-tension ratio.

No-go theorems on localization of gravity around higher codimensional branes in noncompact extra dimensions

We study the brane world scenario of a single brane (or a single stack of branes) with codimension higher than one. When the extra dimensions are not small, localization of gravity around the brane is needed in order to reproduce the observable four-dimensional gravity. We focus on the case of noncompact extra dimensions, where the possibility of localized gravity becomes non-trivial. We show that in large class of gravity models, localization of massless gravity is not possible for codimension-2 branes with at least one noncompact extra dimension. With additional mild assumptions on field backgrounds, we also show that it is not possible for higher codimensional branes with two or more noncompact extra dimensions.

Half-hypermultiplets and incomplete/complete resolutions in F-theory

We consider resolutions of codimension-two enhanced singularities from SO(12) to E7 and from E7 to E8 in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional fibers at the enhanced point exhibit different structures depending on how the colliding 7-brane approaches the stack of gauge 7-branes, as previously observed by Morrison and Taylor in the case of the enhancement from SU(6) to E6. When the colliding brane approaches them as O(s), where s is the coordinate of the base space along the gauge 7-branes, the resolution process ends up with fewer exceptional fibers than naively expected from the Kodaira classification, with a non-Dynkin intersection matrix including half-integral intersection numbers. We confirm that the exceptional fibers at the enhanced point form extremal rays of the cone of the positive weights of the relevant pseudo-real representation, explaining why a half-hypermultiplet arises there. By altering the ordering of the singularities blown up in the process, we obtain, for both SO(12) → E7 and E7 → E8, the intersection diagram on every other row of the corresponding box graphs. We present detailed derivations of the intersection diagrams of the exceptional fibers at the singularity enhanced points by examining how an exceptional curve is lifted up on the chart arising due to the subsequent blowing-up process. When the colliding brane approaches the stack of branes as O(s2), we obtain additional conifold singularity at the enhanced point, which completes the full Dynkin diagram of the enhanced group as was found previously.

Intersecting D-brane stacks and tachyons at finite temperature

In [1] and [2] intersecting D-branes in flat space were studied at finite temperature in the Yang–Mills approximation. The one-loop correction to the tachyon mass was computed and the critical temperature at which the tachyon becomes massless was obtained numerically. In this paper we extend the computation of one-loop two-point amplitude to the case of intersecting stacks of D3-branes in flat space. The motivation for this calculation is to study the strong coupling holographic BCS model proposed in [3] at finite temperature. We show that the analytical results of [1] and [2] can be embedded into this more general setup. The main technicality involved here is keeping track of the extra color factors coming from the unbroken gauge groups. We further discuss the issues involved in the computation of two point amplitude for case of multiple intersecting stacks of branes.

Open strings and electric fields in compact spaces

We analyse open strings with background electric fields in the internal space, T-dual to branes moving with constant velocities in the internal space. We find that the direction of the electric fields inside a two torus, dual to the D-brane velocities, has to be quantised such that the corresponding direction is compact. This implies that D-brane motion in the internal torus is periodic, with a periodicity that can be parametrically large in terms of the internal radii. By S-duality, this is mapped into an internal magnetic field in a three torus, a quantum mechanical analysis of which yields a similar result, i.e. the parallel direction to the magnetic field has to be compact. Furthermore, for the magnetic case, we find the Landau level degeneracy as being given by the greatest common divisor of the flux numbers. We carry on the string quantisation and derive the relevant partition functions for these models. Our analysis includes also the case of oblique electric fields which can arise when several stacks of branes are present. Compact dimensions and/or oblique sectors influence the energy loss of the system through pair-creation and thus can be relevant for inflationary scenarios with branes. Finally, we show that the compact energy loss is always larger than the non-compact one.

Do alien particles exist, and can they be detected?

We may call “alien particles” those particles belonging to the matter/field content of a [Formula: see text]-dimensional brane other than the [Formula: see text]-brane (or stack of branes) sweeping the spacetime in which we live. They can appear in our spacetime at the regions of intersection between our and their brane. They can be identified (or not) as alien matter depending on their properties, on the physical laws governing their evolution in the “homeland” brane, and on the details of our detection techniques.

Deformations on tilted tori and moduli stabilisation at the orbifold point

We discuss deformations of orbifold singularities on tilted tori in the context of Type IIA orientifold model building with D6-branes on special Lagrangian cycles. Starting from $$ {T}^6/\left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_2\right) $$ , we mod out an additional $$ {\mathrm{\mathbb{Z}}}_3 $$ symmetry to describe phenomenologically appealing backgrounds and reduce to $$ {\mathrm{\mathbb{Z}}}_3 $$ and $$ \Omega \mathrm{\mathcal{R}} $$ invariant orbits of deformations. While D6-branes carrying SO(2N) or USp(2N) gauge groups do not constrain deformations, D6-branes with U(N) gauge groups develop non-vanishing D-terms if they couple to previously singular, now deformed cycles. We present examples for both types of D6-branes, and in a three-generation Pati-Salam model on $$ {T}^6/\left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_6^{\prime}\right) $$ we find that ten out of 15 twisted complex structure moduli are indeed stabilised at the orbifold point by the existence of the brane stacks.

A Classification of Long-Range Interactions between Two Stacks of p & p′-Branes

We generalize the computations of the long-range interactions between two parallel stacks of branes to various cases when two stacks of branes are not placed parallel to each other. We classify the nature of interaction (repulsive or attractive) for each special case and this classification can be used to justify the nature of long-range interaction between two complicated brane systems such as brane bound states. We will provide explicit examples in this paper to demonstrate this.

On the 1-loop effective action for the IKKT model and non-commutative branes

We study the one-loop effective action of the IKKT or IIB model on a 4-dimensional non-commutative brane background. The trace-U(1) sector is governed by non-commutativity, and leads - assuming no SUSY breaking - to a higher-derivative effective action. In contrast, the non-Abelian sector at low energies reduces to SU(n) N=4 Super-Yang-Mills on the brane, with a global SO(9,1) symmetry broken spontaneously by the background. In the Coulomb branch, we recover the leading contribution to the Dirac-Born-Infeld (DBI) action, exhibiting a S^5 \times AdS^5 bulk geometry around a stack of branes. SUSY may be broken by compact extra dimensions M^4 x K, leading to an induced gravitational action on M^4 due to the trace-U(1) sector. The one-loop effective action is UV finite on such backgrounds, and the UV/IR mixing is non-pathological.

Global F-theory models: instantons and gauge dynamics

We elucidate certain aspects of F-theory gauge dynamics, due to quantum splitting of certain brane stacks, which are absent in the Type IIB limit. We also provide a working implementation of an algorithm for computing cohomology of line bundles on arbitrary toric varieties. This should be of general use for studying the physics of global Type IIB and F-theory models, in particular for the explicit counting of zero modes for rigid F-theory instantons which contribute to charged matter couplings. We illustrate the discussion by constructing and analyzing in detail a compact F-theory GUT model in which a D-brane instanton generates the top Yukawa coupling non-perturbatively.

Dynamical fine tuning in brane inflation

We investigate a novel mechanism of dynamical tuning of a flat potential in the open string landscape within the context of warped brane-antibrane inflation in type IIB string theory. Because of competing effects between interactions with the moduli stabilizing D7-branes in the warped throat and anti-D3-branes at the tip, a stack of branes gives rise to a local minimum of the potential, holding the branes high up in the throat. As branes successively tunnel out of the local minimum to the bottom of the throat the potential barrier becomes lower and is eventually replaced by a flat inflection point, around which the remaining branes easily inflate. This dynamical flattening of the inflaton potential reduces the need to fine tune the potential by hand, and also leads to successful inflation for a larger range of inflaton initial conditions, due to trapping in the local minimum.

Contact interactions in low scale string models with intersectingD6-branes

We evaluate the tree level four fermion string amplitudes in the TeV string mass scale models with intersecting $D6$-branes. The coefficient functions of contact interactions subsuming the contributions of string Regge resonance and winding mode excitations are obtained by subtracting out the contributions from the string massless and massive momentum modes. Numerical applications are developed for the standard-model-like solution of Cremades, Ibanez, and Marchesano for a toroidal orientifold with four intersecting $D6$-brane stacks. The chirality conserving contact interactions of the quarks and leptons are considered in applications to high-energy collider and flavor changing neutral current phenomenology. The two main free parameters consist of the string and compactification mass scales, ${m}_{s}$ and ${M}_{c}$. Useful constraints on these parameters are derived from predictions for the Bhabha scattering differential cross section and for the observables associated to the mass shifts of the neutral meson systems $K\ensuremath{-}\overline{K}$, $B\ensuremath{-}\overline{B}$, $D\ensuremath{-}\overline{D}$ and the lepton number violating three-body leptonic decays of the charged leptons $\ensuremath{\mu}$ and $\ensuremath{\tau}$.

(D)‐instanton effects in magnetized brane worlds

AbstractWe consider systems of magnetized D9 branes on orbifolds supporting 𝒩 = 1 gauge theories. In such realizations, the matter multiplets arise from “twisted” strings connecting different stacks of branes. The introduction of Euclidean 5‐branes wrapped on the six‐dimensional compact space leads to instanton effects. We examine the interplay between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low‐energy supergravity action which describes the system, including its instanton corrections. This talk is mostly based on [1].

Instanton effects in 𝒩 = 1 brane models and the Kähler metric of twisted matter

We consider locally consistent systems of magnetized D9 branes on an orbifolded six-torus which support = 1 gauge theories. In such realizations, the matter multiplets arise from ``twisted'' strings connecting different stacks of branes. The introduction of Euclidean 5 branes (E5) wrapped on the six-dimensional compact space leads to instanton effects. For instance, if the system is engineered so as to yield SQCD, a single E5 brane may account for the ADS/TVY superpotential. We discuss the subtle interplay that exists between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy action of the = 1 theory. The consistency of this picture allows to obtain information on the Kahler metric of the chiral matter multiplets arising from twisted strings.

D-brane standard model variants and split supersymmetry: Unification and fermion mass predictions

We study D-brane inspired models with U(3) x U(2) x U(1)^N gauge symmetry in the context of split supersymmetry. We consider configurations with one, two and three (N=1,2,3) abelian branes and derive all hypercharge embeddings which imply a realistic particle content. Then, we analyze the implications of split supersymmetry on the magnitude of the string scale, the gauge coupling evolution, the third family fermion mass relations and the gaugino masses. We consider gauge coupling relations which may arise in parallel as well as intersecting brane scenarios and classify the various models according to their predictions for the magnitude of the string scale and the low energy implications. In the parallel brane scenario where the U(1) branes are superposed to U(2) or U(3) brane stacks, varying the split susy scale in a wide range, we find three distinct cases of models predicting a high, intermediate and low string scale, M_S ~ 10^{16} GeV, M_S ~ 10^7 GeV and M_S ~ 10^4 GeV respectively. We further find that in the intermediate string scale model the low energy ratio m_b / m_\tau is compatible with b-\tau Yukawa unification at the string scale. Furthermore, we perform a similar analysis for arbitrary abelian gauge coupling relations at M_S corresponding to possible intersecting brane models. We find cases which predict a string scale of the order M_S \ge 10^{14} GeV that accommodate a right-handed neutrino mass of the same order so that a see-saw type light left-handed neutrino component is obtained in the sub-eV range as required by experimental and cosmological data. Finally, a short discussion is devoted for the gaugino masses and the life-time of the gluino.