Compactifications Of String Theory Research Articles

Firewall black holes and echoes from an action principle

It is often said that there is no gravity theory based on local action principles giving rise to firewall black hole solutions. Additionally, Guo and Mathur 2022 (2205.10921) have cast doubt on the observability of firewall echoes due to closed trapped surface produced by backreaction of macroscopic in-falling wave packets. In this paper, we bring Einstein-Maxwell-Dilaton action as a toy model that serves as counterexample to these assertions. Actions with Maxwell and dilaton fields emerge from several fundamental theories, such as the low energy limit of (super) string theory or Kaluza-Klein compactifications. In these systems, the black hole solution has two curvature singularities. We will show that the outer singularity inside the event horizon can cause significant change to the outside, close to the extremal limit, making a macroscopic reflective barrier near the event horizon that would lead to "observable" gravitational wave echoes in this toy model. Additionally, we also call into question the argument by Guo et al. 2017 (1711.01617) claiming that a very small fraction of the backscattered photons will be able to escape back to infinity from the firewall using these black holes as counterexample.

Logarithmic correction to black hole entropy in universal low-energy string theory models

We calculate the logarithmic correction to the entropy of asymptotically flat and AdS black holes (rotating, non-rotating, charged, and uncharged) embedded in Einstein-Maxwell-dilaton (EMD) theories with U(1)-charged. The leading quantum gravitational corrections are achieved in both extremal and non-extremal limits of black hole temperature by designing a common Euclidean gravity setup that evaluates the “logarithmic term” from one-loop effective actions via heat kernel method-based calculations. EMD theories are universal building blocks of compactified string theory or supergravity models in 4D. For a concrete example, we generalize the entire setup and calculate logarithmic corrections for black holes in U(1)2-charged EMD models intersecting with mathcal{N} = 4 ungauged and gauged bosonic supergravity. In contrast to flat backgrounds, all the AdS4 results are found to be non-topological, providing a wider “infrared window” into the microscopic degrees of freedom of black holes in string theory.

Metastable vacua from torsion and machine learning

By implementing an error function on a Machine Learning algorithm we look for minimal conditions to construct stable Anti de Sitter and de Sitter vacua from dimensional type IIB String theory compactification on Kähler manifolds with torsion. This allows to have contributions to the scalar potential from the five-form flux and from D-branes wrapping torsional cycles, interpreted as non-BPS states. The former implies the possibility to construct stable AdS vacua while the latter constitutes a mechanism to uplift AdS to dS vacua. Particularly we consider {widehat{D5}} non-BPS states to uplift the stable AdS vacua to an (apparently) stable dS minimum. Both results – the generation of an AdS vacuum and the corresponding uplifting to a dS one – are restricted to a certain type of configurations, specifically with the number of O3 orientifolds bounded from below by the number of D3-branes and fluxes. Under these conditions, we report over 170 dS (classical) stable vacua. In all of them, the uplifted effective potential becomes very flat indicating the presence of possible sources of instabilities. We comment on their relationship with the Swampland Conjectures.

Superpotentials from singular divisors

We study Euclidean D3-branes wrapping divisors D in Calabi-Yau orientifold compactifications of type IIB string theory. Witten’s counting of fermion zero modes in terms of the cohomology of the structure sheaf {mathcal{O}}_D applies when D is smooth, but we argue that effective divisors of Calabi-Yau threefolds typically have singularities along rational curves. We generalize the counting of fermion zero modes to such singular divisors, in terms of the cohomology of the structure sheaf {mathcal{O}}_{overline{D}} of the normalization overline{D} of D. We establish this by detailing compactifications in which the singularities can be unwound by passing through flop transitions, giving a physical incarnation of the normalization process. Analytically continuing the superpotential through the flops, we find that singular divisors whose normalizations are rigid can contribute to the superpotential: specifically, {h}_{+}^{bullet}left({mathcal{O}}_{overline{D}}right)=left(1,0,0right) and {h}_{-}^{bullet}left({mathcal{O}}_{overline{D}}right)=left(0,0,0right) give a sufficient condition for a contribution. The examples that we present feature infinitely many isomorphic geometric phases, with corresponding infinite-order monodromy groups Γ. We use the action of Γ on effective divisors to determine the exact effective cones, which have infinitely many generators. The resulting nonperturbative superpotentials are Jacobi theta functions, whose modular symmetries suggest the existence of strong-weak coupling dualities involving inversion of divisor volumes.

Taming the landscape of effective theories

We introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, we propose a Tameness Conjecture that states that all valid effective theories are labelled by a definable parameter space and must have scalar field spaces and coupling functions that are definable using the tame geometry built from an o-minimal structure. We give a brief introduction to tame geometry and describe how it restricts sets, manifolds, and functions. We then collect evidence for the Tameness Conjecture by studying various effective theories arising from string theory compactifications by using some recent advances in tame geometry. In particular, we will exploit the fact that coset spaces and period mappings are definable in an o-minimal structure and argue for non-trivial tameness results in higher-supersymmetric theories and in Calabi-Yau compactifications. As strongest evidence for the Tameness Conjecture over a discrete parameter space, we then discuss a recent theorem stating that the locus of self-dual flux vacua of F-theory admits a tame geometry even if one allows for any flux choice satisfying the tadpole constraint. This result implies the finiteness of self-dual flux vacua in F-theory.

Over-extremal brane shells from string theory?

We demonstrate that, if the usual phenomenological compactifications of IIB string theory with warped throats and anti-branes make sense, there must exist spherical brane shells in 4d that are overcharged. They correspond to classical over-extremal objects but without the usual naked singularities. The objects are made from D3-particles that puff into spherical five-branes that stabilise at finite radii in 4d and whose inside corresponds to the supersymmetric AdS vacuum. One can think of these shells as stabilised Brown–Teitelboim bubbles. We find that these objects can be significantly larger than the string scale depending on the details of the warped compactification.

Tameness, Strings, and the Distance Conjecture

The Distance Conjecture states that an infinite tower of modes becomes exponentially light when approaching an infinite distance point in field space. We argue that the inherent path-dependence of this statement can be addressed when combining the Distance Conjecture with the recent Tameness Conjecture. The latter asserts that effective theories are described by tame geometry and implements strong finiteness constraints on coupling functions and field spaces. By exploiting these tameness constraints we argue that the region near the infinite distance point admits a decomposition into finitely many sectors in which path-independent statements for the associated towers of states can be established. We then introduce a more constrained class of tame functions with at most polynomial asymptotic growth and argue that they suffice to describe the known string theory effective actions. Remarkably, the multi-field dependence of such functions can be reconstructed by one-dimensional linear test paths in each sector near the boundary. In four-dimensional effective theories, these test paths are traced out as a discrete set of cosmic string solutions. This indicates that such cosmic string solutions can serve as powerful tool to study the near-boundary field space region of any four-dimensional effective field theory. To illustrate these general observations we discuss the central role of tameness and cosmic string solutions in Calabi-Yau compactifications of Type IIB string theory.

Generic no-scale inflation inspired from string theory compactifications

We propose the generic no-scale inflation inspired from string theory compactifications. We consider the K\"ahler potentials with an inflaton field $\ensuremath{\varphi}$, as well as one, two, and three K\"ahler moduli. Also, we consider the renormalizable superpotential of $\ensuremath{\varphi}$ in general. We study the spectral index and tensor-to-scalar ratio in details, and find the viable parameter spaces which are consistent with the Planck and BICEP/Keck experimental data on the cosmic microwave background (CMB). The spectral index is ${n}_{s}\ensuremath{\simeq}1\ensuremath{-}2/N\ensuremath{\sim}0.965$ for all models, and the tensor-to-scalar ratio $r$ is $r\ensuremath{\simeq}12/{N}^{2}$, $83/{N}^{4}$ and $4/{N}^{2}$ for the one, two and three moduli models, respectively. The particular $r$ for two moduli model comes from the contributions of the non-negligible higher order term in potential. In the three moduli model, the scalar potential is similar to the global supersymmetry, but the K\"ahler potential is different. The E model with $\ensuremath{\alpha}=1$ and T model with $\ensuremath{\alpha}=1/3$ can be realized in the one modulus model and the three moduli model, respectively. Interestingly, the models with quadratic and quartic potentials still satisfy the current tight bound on $r$ after embedding into no-scale supergravity.

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

The tree-level q-map assigns to a projective special real (PSR) manifold of dimension n-1ge 0, a quaternionic Kähler (QK) manifold of dimension 4n+4. It is known that the resulting QK manifold admits a (3n+5)-dimensional universal group of isometries (i.e. independently of the choice of PSR manifold). On the other hand, in the context of Calabi–Yau compactifications of type IIB string theory, the classical hypermultiplet moduli space metric is an instance of a tree-level q-map space, and it is known from the physics literature that such a metric has an mathrm {SL}(2,{mathbb {R}}) group of isometries related to the mathrm {SL}(2,{mathbb {Z}}) S-duality symmetry of the full 10d theory. We present a purely mathematical proof that any tree-level q-map space admits such an mathrm {SL}(2,{mathbb {R}}) action by isometries, enlarging the previous universal group of isometries to a (3n+6)-dimensional group G. As part of this analysis, we describe how the (3n+5)-dimensional subgroup interacts with the mathrm {SL}(2,{mathbb {R}})-action, and find a codimension one normal subgroup of G that is unimodular. By taking a quotient with respect to a lattice in the unimodular group, we obtain a quaternionic Kähler manifold fibering over a projective special real manifold with fibers of finite volume, and compute the volume as a function of the base. We furthermore provide a mathematical treatment of results from the physics literature concerning the twistor space of the tree-level q-map space and the holomorphic lift of the (3n+6)-dimensional group of universal isometries to the twistor space.

Type IIB flux compactifications with h1,1 = 0

We revisit flux compactifications of type IIB string theory on ‘spaces’ dual to rigid Calabi-Yau manifolds. This rather unexplored part of the string landscapes harbors many interesting four-dimensional solutions, namely supersymmetric mathcal{N} = 1 Minkowski vacua without flat direction and infinite families of AdS vacua, some potentially with unrestricted rank for the gauge group. We also comment on the existence of metastable dS solutions in this setup. We discuss how these solutions fit into the web of swampland conjectures.

Exceptional Algebroids and Type IIA Superstrings

AbstractWe study exceptional algebroids in the context of warped compactifications of type IIA string theory down to n dimensions, with . In contrast to the M‐theory and type IIB case, the relevant algebroids are no longer exact, and their locali moduli space is no longer trivial, but has 5 distinct points. This relates to two possible scalar deformations of the IIA theory. The proof of the local classification shows that, in addition to these scalar deformations, one can twist the bracket using a pair of 1‐forms, a 2‐form, a 3‐form, and a 4‐form. Furthermore, we use the analysis to translate the classification of Leibniz parallelisable spaces (corresponding to maximally supersymmetric consistent truncations) into a tractable algebraic problem. We finish with a discussion of the Poisson–Lie U‐duality and examples given by tori and spheres in 2, 3, and 4 dimensions.

BPS Algebras in 2D String Theory

We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form V_1otimes bar{V}_2, where V_1, V_2 are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications.

An anthropic solution to the cosmological moduli problem

Light moduli fields, gravitationally coupled scalar fields with no classical potential and which are expected to emerge as remnants from string theory compactification, are dangerous to cosmology in that 1. their late-time decays may disrupt successful Big Bang Nucleosynthesis (BBN), 2. they may decay into gravitino pairs which result in violation of BBN constraints or overproduction of lightest SUSY particles (LSPs, assumed to constitute at least a portion of the dark matter in the universe) and 3. they may decay directly into LSPs, resulting in gross DM overproduction. Together, these constitute the cosmological moduli problem (CMP). The combined effects require lightest modulus mass mϕ≳104 TeV, and if the lightest modulus mass mϕ is correlated with the SUSY breaking scale m3/2, then the underlying SUSY model would be highly unnatural. We present a solution to the CMP wherein the lightest modulus initial field strength ϕ0 is anthropically selected to be ϕ0∼10−7mP by the requirement that the dark matter-to-baryonic matter ratio be not-too-far removed from its present value so that sufficient baryons are present in the universe to create observers. In this case, instead of dark matter overproduction via neutralino reannihilation at the modulus decay temperature, the neutralinos inherit the reduced moduli number density, thereby gaining accord with the measured dark matter relic density.

Top-down anatomy of flavor symmetry breakdown

A top-down approach to the flavor puzzle leads to eclectic flavor groups which include modular and traditional flavor symmetries. Based on examples of semirealistic T2/Z3 orbifold compactifications of heterotic string theory, we discuss the breakdown patterns of the eclectic flavor group via the interplay of vacuum expectation values (vevs) of moduli and flavon fields. This leads to an attractive flavor scheme with various possibilities to obtain "flavor hierarchies" through the alignment of these vevs. Despite the fact that the top-down approach gives strong restrictions for bottom-up flavor model building, it seems to be well suited to provide a realistic flavor pattern for quarks and leptons.

Conway subgroup symmetric compactifications redux

We extend the investigation in [1] of special toroidal compactifications of heterotic string theory for which the half-BPS states provide representations of subgroups of the Conway group. We also explore dual descriptions of these theories and find that they are all linked to either F-theory or type IIA string theory on K3 surfaces with symplectic automorphism groups that are the same Conway subgroups as those of the heterotic dual. The matching with type IIA K3 dual theories includes both the matching of symmetry groups and a comparison between the Narain lattice on the heterotic side and the cohomology lattice on the type IIA side. We present twelve examples where we can identify a type IIA dual K3 orbifold theory as the dual description of the heterotic theory. In addition, we include a supplementary Mathematica package that performs most of the computations required for these comparisons.

Emergent strings from infinite distance limits

As a refinement of the Swampland Distance Conjecture, we propose that a quantum gravitational theory in an infinite distance limit of its moduli space either decompactifies, or reduces to an asymptotically tensionless, weakly coupled string theory. We support our claim by classifying, as special cases, the behaviour of M-Theory and Type IIA string theory compactifications on Calabi-Yau three-folds at infinite distances in Kähler moduli space.The analysis comprises three parts: we first classify the possible infinite distance limits in the classical Kähler moduli space of a Calabi-Yau three-fold. Each such limit at finite volume is characterized by a universal fibration structure, for which the generic fiber shrinking in the limit is either an elliptic curve, a K3 surface, or an Abelian surface.In the second part we focus on M-Theory and investigate the nature of the towers of asymptotically massless states that arise from branes wrapped on the shrinking fibers. Depending on which of the three classes of fibrations are considered, we obtain decompactification to F-Theory, or a theory with a unique asymptotically tensionless, weakly coupled heterotic or Type II string, respectively. The latter probes a dual D-manifold which is in general non-geometric. In addition to the intrinsic string excitations, towers of states from M2-branes along non-contractible curves become light and correspond to further wrapping and winding modes of the tensionless heterotic or Type II string.In the third part of the analysis, we consider Type IIA string theory on Calabi-Yau three-folds and show that quantum effects obstruct taking finite volume infinite distance limits in the Kähler moduli space. The only possible infinite distance limit which is not a decompactification limit involves K3-fibrations with string scale fiber volume and gives rise to an emergent tensionless heterotic string.

The tadpole conjecture at large complex-structure

The tadpole conjecture by Bena, Blåbäck, Graña and Lüst effectively states that for string-theory compactifications with a large number of complex-structure moduli, not all of these moduli can be stabilized by fluxes. In this note we study this conjecture in the large complex-structure regime using statistical data obtained by Demirtas, Long, McAllister and Stillman for the Kreuzer-Skarke list. We estimate a lower bound on the flux number in type IIB Calabi-Yau orientifold compactifications at large complex-structure and for large h2,1, and our results support the tadpole conjecture in this regime.

Axion-like particle oscillations

String theory compactifications may generate many light axion-like particles (ALPs) with weak couplings to electromagnetism. In general, a large number of ALPs may exist, with a linear combination having a potentially observable coupling to electromagnetism. The basis in which only one ALP couples to electromagnetism is in general misaligned with the mass basis. This leads to mixing between the `electromagnetic' ALP and a number of `hidden' ALPs that do not interact directly with the photon. The process is analagous to neutrino oscillations. I will discuss the phenomenological consequences of this mixing for astrophysical ALP signals, in particular showing that it may significantly reduce the predicted signal in experiments such as the CERN Axion Solar Telescope.

A gravitational action with stringy Q and R fluxes via deformed differential graded Poisson algebras

We study a deformation of a 2-graded Poisson algebra where the functions of the phase space variables are complemented by linear functions of parity odd velocities. The deformation is carried by a 2-form B-field and a bivector Π, that we consider as gauge fields of the geometric and non-geometric fluxes H, f, Q and R arising in the context of string theory compactification. The technique used to deform the Poisson brackets is widely known for the point particle interacting with a U(1) gauge field, but not in the case of non-abelian or higher spin fields. The construction is closely related to Generalized Geometry: with an element of the algebra that squares to zero, the graded symplectic picture is equivalent to an exact Courant algebroid over the generalized tangent bundle E ≅ TM ⊕ T∗M, and to its higher gauge theory. A particular idempotent graded canonical transformation is equivalent to the generalized metric. Focusing on the generalized differential geometry side we construct an action functional with the Ricci tensor of a connection on covectors, encoding the dynamics of a gravitational theory for a contravariant metric tensor and Q and R fluxes. We also extract a connection on vector fields and determine a non-symmetric metric gravity theory involving a metric and H-flux.

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.