IIB String Theory Research Articles

Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions

Compactification of M-theory and of IIB string theory on threefold canonical singularities gives rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. The resolutions and deformations of the singularities encode salient features of the SCFTs and of their moduli spaces. In this paper, we build on Part 0 of this series [1] and further explore the physics of SCFTs arising from isolated hypersurface singularities. We study in detail these canonical isolated hypersurface singularities that admit a smooth Calabi-Yau (crepant) resolution. Their 5d and 4d physics is discussed and their 3d reduction and mirrors (the magnetic quivers) are determined in many cases. As an explorative tool, we provide a Mathematica code which computes key quantities for any canonical isolated hypersurface singularity, including the 5d rank, the 4d Coulomb branch spectrum and central charges, higher-form symmetries in 4d and 5d, and crepant resolutions.

Holographic evidence for nonsupersymmetric conformal manifolds

We provide the first holographic evidence for the existence of a nonsupersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter nonsupersymmetric deformation of a supersymmetric AdS nongeometric background in type IIB string theory. We prove that the nonsupersymmetric backgrounds are perturbatively stable and also do not suffer from various nonperturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections.

GMOR relation for a QCD-like theory from S-duality

Following [1] we study a QCD-like gauge theory using a non-supersymmetric setup in type IIB string theory. The setup includes an O3 plane and N D3 anti-branes and it realises a USp(2N) ‘electric’ gauge theory with four “quarks” in the two-index antisymmetric representation and six heavy scalars in the adjoint representation. Using S-duality we obtain a dual ‘magnetic’ theory that includes SO(2N−1) gauge theory with six scalars in the adjoint representation and four heavy “quarks” in the two-index symmetric representation. The dual theory provides a description of confinement and dynamical symmetry breaking of the form SU(4)→SO(4). We extend the results of [1] by adding masses to the quarks in the electric side and deriving parts of the chiral Lagrangian using the dual magnetic theory. In particular, we derive the Gell-Mann-Oakes-Renner (GMOR) relation for Nambu-Goldstone bosons (pions) using the magnetic theory.

The Gibbons–Hawking Ansatz in Generalized Kähler Geometry

We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and a biholomorphic $S^1$ action which generalizes the classic Gibbons-Hawking ansatz for invariant hyperK\"ahler manifolds, and allows for the choice of one arbitrary function. By imposing the generalized K\"ahler-Ricci soliton equation, or equivalently the equations of type IIB string theory, the construction becomes rigid, and we classify all complete solutions with the smallest possible symmetry group.

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.

Non-supersymmetric AdS6 and the swampland

We discuss infinite families of non-supersymmetric AdS6 solutions in Type IIB string theory. They are siblings of supersymmetric solutions which are associated with (p, q) 5-brane webs and holographically dual to 5d SCFTs engineered by those brane webs. The non-supersymmetric backgrounds carry identical 5-brane charges and are connected to the supersymmetric ones by RG flows. We study the stability of the non-supersymmetric solutions, identifying perturbative and non-perturbative decay channels for all the backgrounds explicitly available. We also identify likely decay mechanisms for solutions that have not been constructed explicitly but may be expected to exist based on brane web considerations. Finally, we exclude scale separation by constructing universal spin 2 modes with masses comparable to the mass-scale of the cosmological constant.

Small cosmological constants in string theory

We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α′ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10−123 in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.

Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds

We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the predictions based on S-duality, mirror symmetry and supersymmetry.

Normalization of type IIB D-instanton amplitudes

We compute the normalization of single D-instanton amplitudes in type IIB string theory and show that the result agrees with the prediction of S-duality due to Green and Gutperle.

1-form symmetry, isolated mathcal{N} = 2 SCFTs, and Calabi-Yau threefolds

We systematically study 4D mathcal{N} = 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ℂ4. We show that if a theory in this class has no mathcal{N} = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an mathcal{N} = 2 SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying a<frac{1}{24}left(15r+2fright) and c<frac{1}{6}left(3r+fright) (where r is the complex dimension of the Coulomb branch, and f is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D mathcal{N} = 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

Muti-instanton amplitudes in type IIB string theory

We compute the normalization of the multiple D-instanton amplitudes in type IIB string theory and show that the result agrees with the prediction of S-duality due to Green and Gutperle.

Modular invariant holographic correlators for mathcal{N} = 4 SYM with general gauge group

We study the stress tensor four-point function for mathcal{N} = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

Finding AdS5\xd7 S5 in 2+1 dimensional SCFT physics

We study solutions of type IIB string theory dual to mathcal{N} = 4 supersymmetric Yang-Mills theory on half of ℝ3,1 coupled to holographic three-dimensional superconformal field theories (SCFTs) at the edge of this half-space. The dual geometries are asymptotically AdS5×S5 with boundary geometry ℝ2,1×ℝ+, with a geometrical end-of-the-world (ETW) brane cutting off the other half of the asymptotic region of the would-be Poincaré AdS5×S5. We show that by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily far towards the missing asymptotic region, recovering the “missing” half of Poincaré AdS5×S5. We also show that there are 3D SCFTs whose dual includes a wedge of Poincaré AdS5×S5 with an angle arbitrarily close to π, with geometrical ETW branes on either side.

De Sitter Space as a Glauber‐Sudarshan State: II

AbstractWe provide further evidence to support the fact that a four‐dimensional effective field theory description with de Sitter isometries in IIB string theory, overcoming the no‐go and the swampland criteria, can only exist if de Sitter space is realized as a Glauber‐Sudarshan state. We show here that this result is independent of the choice of de Sitter slicings. The Glauber‐Sudarshan state, constructed by shifting the interacting vacuum in the M‐theory uplift of the scenario, differs from a standard coherent state in QFT in the sense that the shape and size of the state changes with respect to time, implying changes in the graviton and the flux quanta. Despite this, the expectation values of the graviton and flux operators in such a state reproduce the exact de Sitter background, as long as we are within the temporal bound set by the onset of the strong coupling in the dual type IIA side, and satisfy the corresponding Schwinger‐Dyson's equations in the presence of hierarchically controlled perturbative and non‐perturbative quantum corrections.Additionally, we provide a detailed study of the fluxes supporting the Glauber‐Sudarshan state in the M‐theory uplift of the IIB scenario. We show explicitly how the Bianchi identities, anomaly cancellation and flux quantization conditions, along‐with the constraints from the Schwinger‐Dyson's equations, conspire together to provide the necessary temporal dependences to support such a state in full M‐theory. We also discuss how our analysis points towards a surprising connection to the four‐dimensional null energy condition, for a Friedman‐Lemaitre‐Robertson‐Walker state in the IIB side, as a consistency condition for the existence of an effective field theory description in M‐theory.

Wilson loops in mathcal{N} = 4 SO(N) SYM and D-branes in AdS5 \xd7 \u211d\u21195

We study the half-BPS circular Wilson loop in mathcal{N} = 4 super Yang-Mills with orthogonal gauge group. By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of SO(N). We focus on the large N limit and present some simple quantitative tests of the duality with type IIB string theory in AdS5× ℝℙ5. In particular, we show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory object, which is expected to be a D5-brane wrapping a ℝℙ4 subspace of ℝℙ5. We also briefly discuss the large N, large λ limits of the SO(N) Wilson loop in the symmetric/antisymmetric representations and their D3/D5-brane duals. Finally, we use the D5-brane description to extract the leading strong coupling behavior of the “bremsstrahlung function” associated to a spinor probe charge, or equivalently the normalization of the two-point function of the displacement operator on the spinor Wilson loop, and obtain agreement with the localization prediction.

The moduli space of non-abelian vortices in Yang–Mills–Chern–Simons–Higgs theory

We determine the dimension of the moduli space of non-abelian vortices in Yang–Mills–Chern–Simons–Higgs theory in 2 + 1 dimensions for gauge groups with G′ being an arbitrary semi-simple group and n 0 the greatest common divisor of the abelian charges of the G′ invariants. The calculation is carried out using a Callias-type index theorem, the moduli matrix approach and a D-brane setup in type IIB string theory. We prove that the index theorem gives the number of zeromodes or moduli of the non-abelian vortices, extend the moduli matrix approach to the Yang–Mills–Chern–Simons–Higgs theory and finally derive the effective Lagrangian of Collie and Tong using string theory.

IIB String Theory and Sequestered Inflation

AbstractWe develop sequestered inflation models, where inflation occurs along flat directions in supergravity models derived from type IIB string theory. It is compactified on a orientifold with generalized fluxes and O3/O7‐planes. At Step I, we use flux potentials which 1) satisfy tadpole cancellation conditions and 2) have supersymmetric Minkowski vacua with flat direction(s). The 7 moduli are split into heavy and massless Goldstone multiplets. At Step II we add a nilpotent multiplet and uplift the flat direction(s) of the type IIB string theory to phenomenological inflationary plateau potentials: α‐attractors with 7 discrete values . Their cosmological predictions are determined by the hyperbolic geometry inherited from string theory. The masses of the heavy fields and the volume of the extra dimensions change during inflation, but this does not affect the inflationary dynamics.

Topological stars, black holes and generalized charged Weyl solutions

We construct smooth static bubble solutions, denoted as topological stars, in five-dimensional Einstein-Maxwell theories which are asymptotic to ℝ1,3×S1. The bubbles are supported by allowing electromagnetic fluxes to wrap smooth topological cycles. The solutions live in the same regime as non-extremal static charged black strings, that reduce to black holes in four dimensions. We generalize to multi-body configurations on a line by constructing closed-form generalized charged Weyl solutions in the same theory. Generic solutions consist of topological stars and black strings stacked on a line, that are wrapped by electromagnetic fluxes. We embed the solutions in type IIB String Theory on S1×T4. In this framework, the charged Weyl solutions provide a novel class in String Theory of multiple charged objects in the non-supersymmetric and non-extremal black hole regime.

Resolving spacetime singularities in flux compactifications & KKLT

In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure SU(N) super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of n such exotic branes is given by the (A1, An−1) Argyres-Douglas theory. Moreover, the splitting of the perturbative (in α′) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of mathcal{O} (1) Einstein frame volume. While this region generically takes up an mathcal{O} (1) fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential dynamically ensures that the 4d effective field theory of KKLT remains valid nevertheless.

Systematics of the \u03b1\u2032 expansion in F-theory

Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate (α′)even corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that (α′)odd effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from (α′)3 effects, modulo potential logarithmic corrections.