IIB String Theory Research Articles

Towards bootstrapping F-theory

We consider type IIB string theory with N D3 branes and various configurations of sevenbranes, such that the string coupling gs is fixed to a constant finite value. These are the simplest realizations of F-theory, and are holographically dual to rank N Argyres-Douglas conformal field theories (CFTs) with SU(2) and SU(3) flavor groups, and Minahan-Nemeschansky CFTs with E6, E7 and E8 flavor groups. We use the Seiberg-Witten curves of these theories to compute the mass deformed sphere free energy F (m) at large N in terms of novel matrix models with non-polynomial potentials. We show how F (m) can be used along with the analytic bootstrap to fix the large N expansion of flavor multiplet correlators in these CFTs, which are dual to scattering of gluons on AdS5 × S3, and in the flat space limit determine the effective theory of sevenbranes in F-theory. As a first step in this program, we use the matrix models to compute the log N term in F (m) and thereby fix the logarithmic threshold in the AdS5 × S3 holographic correlator, which matches the flat space prediction.

Giant graviton expansions and ETW brane

We study the giant gravitons in the AdS4 bagpipe geometries involving end-of-the-world (ETW) brane constructed by a single 5-brane and either two stacks or one stack of D3-branes in Type IIB string theory. From the exact formulae and giant graviton expansions of the half-indices for the half-BPS boundary conditions and interfaces 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 super Yang-Mills theory, we obtain the BPS spectra of the fluctuation modes of the AdS4 bagpipe geometries including the ETW brane region.

Hidden conformal symmetry in AdS2×S2 beyond tree level

Correlators of N=2 hypermultiplets with two-derivative interactions in AdS2×S2 exhibit a hidden four-dimensional conformal symmetry which allows one to repackage all tree-level four-point correlators into a single four-dimensional object corresponding to a contact diagram arising from a massless ϕ4 theory in AdS2×S2. This theory serves as a toy model for IIB string theory in AdS5×S5 and is interesting in its own right because AdS2×S2 describes the near-horizon limit of extremal black holes in four dimensions. We argue that, after acting with an SU(1,1)×SU(2) Casimir, all one-loop correlators can similarly be encoded by a four-dimensional function which arises from a one-loop scalar bubble diagram in AdS2×S2, explaining how the hidden conformal symmetry extends beyond tree level. Finally, we conjecture a scalar effective field theory with a two-derivative interaction in AdS2×S2 whose Witten diagrams should directly reproduce four-point correlators to all loops without acting with Casimirs. Published by the American Physical Society 2024

Noninvertible symmetries in 2D from type IIB string theory

We propose a top-down approach to noninvertible symmetries in two-dimensional quantum field theories and their three-dimensional (3D) associated symmetry topological field theories. We focus on the gauge theory engineered on D1-branes probing a particular Calabi-Yau 4-fold singularity. We show how to derive the symmetry topological field theory, a 3D Dijkgraaf-Witten theory, from the IIB supergravity under dimensional reduction. We also identify branes behind the noninvertible topological lines by dimensionally reducing their world volume actions. The action of noninvertible lines on charged local operators is then realized as the Hanany-Witten transition. Published by the American Physical Society 2024

Glimmers from the axiverse

We study axion-photon couplings in compactifications of type IIB string theory. We find that these couplings are systematically suppressed compared to the inverse axion periodicity, as a result of two effects. First, couplings to the QED theta angle are suppressed for axion mass eigenstates that are light compared to the mass scale set by stringy instantons on the cycle supporting QED. Second, in compactifications with many axions the intersection matrix is sparse, making kinetic mixing weak. We study the resulting phenomenology in an ensemble of 200,000 toy models constructed from the Kreuzer-Skarke database up to the maximum Hodge number h1,1 = 491. We examine freeze-in production and decay of thermal axions, birefringence of the cosmic microwave background, X-ray spectrum oscillations, and constraints on the QCD axion from supernovae. We conclude that compactifications in this corner of the landscape involve many invisible axions, as well as a handful that may be detectable via photon couplings.

Asymptotic symmetries from the string worldsheet

In IIB string theory on AdS3 background with NS-NS fluxes, we show that Brown-Henneaux asymptotic Killing vectors can be derived by requiring both the worldsheet equations of motion and Virasoro constraints are preserved near the asymptotic boundary of the target spacetime. The charges on the worldsheet that generate the corresponding transformations can be written down in both the Lagrangian formalism and Hamiltonian formalism. This provides a method of studying asymptotic symmetry of the target spacetime directly from worldsheet string theories, without using results from the supergravity limit. As an example, we apply this method to flat spacetime in three dimensions and obtain the BMS3 generators on the worldsheet theory.

Worldsheet contributions to instantons in string effective field theories

The D-instantons in [Formula: see text] theory can contribute to the string effective action. The relation with the D-instanton term in Type IIB string theory will be clarified. The equation of the scalar field is projected to the two-dimensional worldsheet, on which a [Formula: see text] conformal field theory may be formulated. The energies of primary states in a minimal [Formula: see text] theory coupled to a [Formula: see text] topological string are evaluated and compared with the particle spectrum.

Single-valuedness of the AdS Veneziano amplitude

We consider the Veneziano amplitude for the scattering of gluons in type IIB string theory on AdS5 × S5/ℤ2 in the presence of D7 branes. On general grounds curvature corrections around flat space can be thought of as arising from the extra insertion of soft gravitons. This naturally leads to an open string world-sheet representation with the extra insertion of single-valued functions evaluated on the real line. We check that the recently obtained first curvature correction is of this form and use this new constraint to compute the second curvature correction of the AdS Veneziano amplitude.

Exact moduli spaces for 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} = 2, D = 5 freely acting orbifolds

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in five dimensions with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We argue that no quantum corrections to these moduli spaces arise. We focus on examples in which all moduli are in the NS-NS sector, while all fields from the R-R sector become massive. The full symmetry group of the moduli space is then determined by the subgroup of the T-duality group that survives the orbifold action. We illustrate this for freely acting orbifolds of type IIB string theory on T5 with 0, 1 or 2 hypermultiplets.

Constraints on the topology of Type IIB string theory

We discuss some topological constraints on Type IIB string theory that cannot be described by elementary characteristic classes. Anomaly cancellation of the worldvolume theory of a D3-brane requires a shifted Dirac quantization condition of the Ramond-Ramond 5-form flux. However, the required shift is sometimes inconsistent depending on the topology of spacetime backgrounds. The obstruction to the existence of a shifted quantization is described by a degree-6 cohomology class whose definition involves spin structure of spacetime manifolds. The cohomology class is interpreted as a background D3-charge, and the Gauss law constraint requires inclusion of additional D3-branes to cancel it.

Exact results for giant graviton four-point correlators

We study the four-point correlator O2O2DD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left\\langle {\\mathcal{O}}_2{\\mathcal{O}}_2\\mathcal{DD}\\right\\rangle $$\\end{document} 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 super Yang-Mills theory (SYM) with SU(N) gauge group, where O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{O}}_2 $$\\end{document} represents the superconformal primary operator with dimension two, while D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{D} $$\\end{document} denotes a determinant operator of dimension N, which is holographically dual to a giant graviton D3-brane extending along S5. We analyse the integrated correlator associated with this observable, obtained after integrating out the spacetime dependence over a supersymmetric invariant measure. Similarly to other classes of integrated correlators 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, this integrated correlator can be computed through supersymmetric localisation on the four-sphere. Employing matrix-model recursive techniques, we demonstrate that the integrated correlator can be reformulated as an infinite sum of protected three-point functions with known coefficients. This insight allows us to circumvent the complexity associated with the dimension-N determinant operator, significantly streamlining the large-N expansion of the integrated correlator. In the planar limit and beyond, we derive exact results for the integrated correlator valid for all values of the ’t Hooft coupling, and investigate the resurgent properties of their strong coupling expansion. Additionally, in the large-N expansion with fixed (complexified) Yang-Mills coupling, we deduce the SL(2, ℤ) completion of these results in terms of the non-holomorphic Eisenstein series. The proposed modular functions are confirmed by explicit instanton calculations from the matrix model, and agree with expectations from the holographic dual picture of known results in type IIB string theory.

One-loop quantization of Euclidean D3-branes in holographic backgrounds

In this note we analyze the semi-classical quantization of D3-branes in three different holographic backgrounds in type IIB string theory. The first background is Euclidean AdS5 with S1× S3 boundary accompanied with a twist to preserve supersymmetry. We work out the spectrum of fluctuations around the classical D3-brane configuration, compute its one-loop partition function, and match to the non-perturbative correction to the superconformal index 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. We then study Euclidean D3-branes in the Pilch-Warner geometry dual to the IR Leigh-Strassler fixed point 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} = 1* with the aim to find non-perturbative corrections to its index. Finally we study Euclidean D3-branes in the non-geometric 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} = 2 J-fold background which is dual to the gauging of the 3D Gaiotto-Witten SCFT.

Binary AdS black holes coupled to a bath in Type IIB

We construct Type IIB string theory setups which, via double holography, realize two gravitational systems in separate AdS spaces which interact with each other and with a non-gravitational bath. We employ top-down string theory solutions with concrete field theory duals in the form of 4d \\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 BCFTs and a first-principles notion of double holography. The setups are used to realize pairs of ‘near’ and ‘far’ black holes from the perspective of the bath, which exchange Hawking radiation with each other and radiate into the bath. We identify three phases for the entropy in the bath characterized as no island, partial island and full island, and discuss the entropy curves. The setups differ from the black hole binaries observed in gravitational wave experiments but may capture certain aspects.

Spectral flow and localisation in AdS3 string theory

We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × \U0001d54b4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory.

Bethe Ansatz for the superconformal index with unequal angular momenta

A few years ago it was shown that the superconformal index of the N=4 supersymmetric SU(N) Yang-Mills theory in the large N limit matches with the entropy of 1/16-supersymmetric black holes in type IIB string theory on AdS5×S5. In some cases, an even more detailed match between the two sides is possible. When the two angular momentum chemical potentials in the index are equal, the superconformal index can be written as a discrete sum of Bethe ansatz solutions, and it was shown that specific terms in this sum are in a one-to-one correspondence to stable black hole solutions, and that the matching can be extended to nonperturbative contributions from wrapped D3-branes. A Bethe ansatz approach to computing the superconformal index exists also when the ratio of the angular momentum chemical potentials is any rational number, but in those cases it involves a sum over a very large number of terms (growing exponentially with N). Benini showed that a specific one of these terms matches with the black hole, but the role of the other terms is not clear. In this paper we analyze some of the additional contributions to the index in the Bethe ansatz approach, and we find that their matching to the gravity side is much more complicated than in the case of equal chemical potentials. In particular, we find some contributions that are larger than the one that was found to match the black holes, in which case they must cancel with other large contributions. We give some evidence that cancellations of this type are possible, but we leave a full understanding of how they work to the future. Published by the American Physical Society 2024

On AdS/CFT duality in the twisted sector of string theory on AdS5× S5/ℤ2 orbifold background

We consider type IIB string theory on an AdS5 × S5/ℤ2 orbifold background, which should be dual to 4d 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} = 2 superconformal SU(N) × SU(N) gauge theory with two bi-fundamental hypermultiplets. The correlator of two chiral BPS operators from the twisted sector of this quiver CFT exhibits non-trivial dependence on the ’t Hooft coupling λ already in the planar limit. This dependence was recently determined using localisation and the expansion at large λ contains a subleading contribution proportional to ζ(3)λ−3/2. We address the question of how to reproduce this correction on the string theory side by starting with the ζ(3)α′3 term in the type IIB string effective action. We find a regular solution of type IIB supergravity which represents a resolution of the AdS5 × S5/ℤ2 orbifold and demonstrate that the relevant light twisted sector states may be identified as additional supergravity 2-form modes “wrapping” a finite 2-cycle in the resolution space. Reproducing the structure of the gauge theory result becomes more transparent in the large R-charge or BMN-like limit in which the resolved background takes a pp-wave form with the transverse space being a product of ℝ4 and the Eguchi-Hanson space.

S-Duality and the Universal Isometries of Instanton Corrected q-Map Spaces

Given a conical affine special Kähler manifold together with a compatible mutually local variation of BPS structures, one can construct a quaternionic-Kähler (QK) manifold. We call the resulting QK manifold an instanton corrected c-map space. Our main aim is to study the isometries of a subclass of instanton corrected c-map spaces associated to projective special real manifolds with a compatible mutually local variation of BPS structures. We call the latter subclass instanton corrected q-map spaces. In the setting of Calabi–Yau compactifications of type IIB string theory, instanton corrected q-map spaces are related to the hypermultiplet moduli space metric with perturbative corrections, together with worldsheet, D(-1) and D1 instanton corrections. In the physics literature, it has been shown that the hypermultiplet metric with such corrections must have an SL(2,Z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{SL}(2,{\\mathbb {Z}})$$\\end{document} acting by isometries, related to S-duality. We give a mathematical treatment of this result, specifying under which conditions instanton corrected q-map spaces carry an action by isometries by SL(2,Z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{SL}(2,{\\mathbb {Z}})$$\\end{document} or some of its subgroups. We further study the universal isometries of instanton corrected q-map spaces, and compare them to the universal isometries of tree-level q-map spaces. Finally, we give an explicit example of a non-trivial instanton corrected q-map space with full SL(2,Z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{SL}(2,{\\mathbb {Z}})$$\\end{document} acting by isometries and admitting a quotient of finite volume by a discrete group of isometries.

Shifted convolution sums motivated by string theory

In [2], it was conjectured that a particular shifted sum of even divisor sums vanishes, and in [11], a formal argument was given for this vanishing. Shifted convolution sums of this form appear when computing the Fourier expansion of coefficients for the low energy scattering amplitudes in type IIB string theory [7] and have applications to subconvexity bounds of L-functions. In this article, we generalize the argument from [11] and rigorously evaluate shifted convolution of the divisor functions of the form ∑n1,n2∈Z∖{0}n1+n2=nσr1(n1)σr2(n2)|n1|P and ∑n1,n2∈Z∖{0}n1+n2=nσr1(n1)σr2(n2)|n1|Qlog⁡|n1| where σν(n)=∑d|ndν. In doing so, we derive exact identities for these sums and conjecture that particular sums similar to but different from the one found in [2] will also vanish.

The planar limit of the 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} = 2 E-theory: numerical calculations and the large λ expansion

We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d 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} = 2 superconformal SU(N) YM theory with hypermultiplets in the symmetric and antisymmetric representations of the gauge group. This so called E theory is closely related to 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 has a holographic description in terms of a ℤ2 orientifold of AdS5 × S5. Using recent matrix model results based on supersymmetric localization we develop efficient numerical methods to calculate two- and three-point functions of certain single trace operators as well as 1/2-BPS Wilson loop expectation values as a function of the ’t Hooft coupling λ. We use our numerical results to arrive at simple analytic expressions for these correlators valid up to sixth order in the λ−1/2 strong coupling expansion. These results provide explicit field theory predictions for the α′ corrections to the supergravity approximation of type IIB string theory on the AdS5 × S5/ℤ2 orientifold.

R7-branes as charge conjugation operators

R7-branes are a class of recently discovered nonsupersymmetric real codimension-two duality defects in type IIB string theory predicted by the swampland cobordism conjecture. For type IIB realizations of 6D SCFTs with N=(2,0) supersymmetry, wrapping an R7-brane “at infinity” leads to a topological operator associated with a zero-form charge conjugation symmetry that squares to the identity. Similar considerations hold for those theories obtained from further toroidal compactification, but this can be obstructed by bundle curvature effects. Using some minimal data on the topological sector of the R7-branes, we extract the associated fusion rules for these charge conjugation operators. More broadly, we sketch a top down realization of various topological operators/interfaces associated with C, R, and T transformations. We also use holography to provide strong evidence for the existence of the R7-brane which is complementary to the cobordism conjecture. Similar considerations apply to other string-realized QFTs with symmetry operators constructed via nonsupersymmetric branes which carry a conserved charge. Published by the American Physical Society 2024