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The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated mapping radii numerically. We also train a neural network distinguishing vertex from Feynman region. As a check, 4-tachyon contact term in the tachyon potential is computed and a good agreement with the results in the literature is observed. We argue that our algorithm is manifestly independent of number of punctures and scaling it to characterize the geometry of n-string contact interaction is feasible. [ABSTRACT FROM AUTHOR]

We define the notion of Y-algebroids, generalising the Lie, Courant, and exceptional algebroids that have been used to capture the local symmetry structure of type II string theory and M-theory compactifications to D ≥ 5 dimensions. Instead of an invariant inner product, or its generalisation arising in exceptional algebroids, Y-algebroids are built around a specific type of tensor, denoted Y , that provides exactly the necessary properties to also describe compactifications to D = 4 dimensions. We classify "M-exact" E7-algebroids and show that this precisely matches the form of the generalised tangent space of E7(7) × ℝ+-generalised geometry, with possible twists due to 1-, 4- and 7-form fluxes, corresponding physically to the derivative of the warp factor and the M-theory fluxes. We translate the notion of generalised Leibniz parallelisable spaces, relevant to consistent truncations, into this language, where they are mapped to so-called exceptional Manin pairs. We also show how to understand Poisson-Lie U-duality and exceptional complex structures using Y-algebroids. [ABSTRACT FROM AUTHOR]

We construct Poisson bracket relations between the operators which generate the chiral ring of the Coulomb branch of certain 3d N = 4 quiver gauge theories. In the case where the Coulomb branch is a free space, ADE Klein singularity, or the minimal A2 nilpotent orbit, we explicitly compute the Poisson brackets between the generators using either inherited properties of the abstract Coulomb branch variety, or the expected charges of these operators under the global symmetry (known through use of the monopole formula). We also conjecture Poisson brackets for Higgs branches that originate from 6d theories with tensionless strings or 5d theories with massless instantons for which the HWG is known, based on representation theoretic and operator content constraints known from the study of their magnetic quiver. [ABSTRACT FROM AUTHOR]

In this article, we first prove the integrality of an explicit disc counting formula obtained by Panfil and Sulkowski for a class of toric Calabi-Yau manifolds named generalized conifolds. Then, motivated by the integrality structures in open topological string theory, we introduce a mathematical notion of "quantum 2-function" which can be viewed as the quantization of the notion of "2-function" introduced by Schwarz, Vologod-sky and Walcher. Finally, we provide a basic example of quantum 2-function and discuss the quantization of 2-functions. [ABSTRACT FROM AUTHOR]

We study the topological G2 and Spin(7) strings at 1-loop. We define new double complexes for supersymmetric NSNS backgrounds of string theory using generalised geometry. The 1-loop partition function then has a target-space interpretation as a particular alternating product of determinants of Laplacians, which we have dubbed the analytic torsion. In the case without flux where these backgrounds have special holonomy, we reproduce the worldsheet calculation of the G2 string and give a new prediction for the Spin(7) string. We also comment on connections with topological strings on Calabi-Yau and K3 backgrounds. [ABSTRACT FROM AUTHOR]

We propose a new way to compute the genus zero Gopakumar-Vafa invariants for two families of non-toric non-compact Calabi-Yau threefolds that admit simple flops: Reid's Pagodas, and Laufer's examples. We exploit the duality between M-theory on these threefolds, and IIA string theory with D6-branes and O6-planes. From this perspective, the GV invariants are detected as five-dimensional open string zero modes. We propose a definition for genus zero GV invariants for threefolds that do not admit small crepant resolutions. We find that in most cases, non-geometric T-brane data is required in order to fully specify the invariants. [ABSTRACT FROM AUTHOR]

Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of 'trinion' singularities which exhibit these properties. In Type IIB, they give rise to 4d N = 2 SCFTs that we call D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as 'ugly' components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver 'bad'. We propose a way to redeem the badness of these quivers using a class S realization. We also discover new S-dualities between different D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT. [ABSTRACT FROM AUTHOR]

We derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action to first order in α′ using Wald's formalism. We carefully take into account all the symmetries of the theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant entropy formula in which all the terms can be computed explicitly. An entropy formula with these properties allows unambiguous calculations of macroscopic black-hole entropies to first order in α′ that can be reliably used in a comparison with the microscopic ones. Such a formula was still lacking in the literature. In the proof we use momentum maps to define covariant variations and Lie derivatives and restricted generalized zeroth laws which state the closedness of certain differential forms on the bifurcation sphere and imply the constancy of the associated potentials on it. We study the relation between our entropy formula and other formulae that have been used in the literature. [ABSTRACT FROM AUTHOR]

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on 't Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra. [ABSTRACT FROM AUTHOR]

We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in ℙ4. [ABSTRACT FROM AUTHOR]

We make a proposal for calculating refined Gopakumar-Vafa numbers (GVN) on elliptically fibered Calabi-Yau 3-folds based on refined holomorphic anomaly equations. The key examples are smooth elliptic fibrations over (almost) Fano surfaces. We include a detailed review of existing mathematical methods towards defining and calculating the (unrefined) Gopakumar-Vafa invariants (GVI) and the GVNs on compact Calabi-Yau 3-folds using moduli of stable sheaves, in a language that should be accessible to physicists. In particular, we discuss the dependence of the GVNs on the complex structure moduli and on the choice of an orientation. We calculate the GVNs in many instances and compare the B-model predictions with the geometric calculations. We also derive the modular anomaly equations from the holomorphic anomaly equations by analyzing the quasi-modular properties of the propagators. We speculate about the physical relevance of the mathematical choices that can be made for the orientation. [ABSTRACT FROM AUTHOR]

We discuss the extent to which numerical techniques for computing approximations to Ricci-flat metrics can be used to investigate hierarchies of curvature scales on Calabi-Yau manifolds. Control of such hierarchies is integral to the validity of curvature expansions in string effective theories. Nevertheless, for seemingly generic points in moduli space it can be difficult to analytically determine if there might be a highly curved region localized somewhere on the Calabi-Yau manifold. We show that numerical techniques are rather efficient at deciding this issue. [ABSTRACT FROM AUTHOR]

We construct a family of hyperbolic string vertices in the oriented open-closed string field theory, generalizing the recent result on hyperbolic closed string vertices by Costello and Zwiebach. The vertices are described by certain bordered hyperbolic surfaces and we explain relevant collar theorems which provide restrictions on the systolic conditions for the hyperbolic vertices. We also give explicit descriptions of the vertices for all zero and one-dimensional moduli spaces. [ABSTRACT FROM AUTHOR]

In this work we study the phase structure of skew symplectic sigma models, which are a certain class of two-dimensional N = ( 2 , 2 ) non-Abelian gauged linear sigma models. At low energies some of them flow to non-linear sigma models with Calabi–Yau target spaces, which emerge from non-Abelian strong coupling dynamics. The observed phase structure results in a non-trivial duality proposal among skew symplectic sigma models and connects non-complete intersection Calabi–Yau threefolds–that are non-birational among another–in a common quantum Kähler moduli space. As a consequence we find non-trivial identifications of spectra of topological B-branes, which from a modern algebraic geometry perspective imply derived equivalences among Calabi–Yau varieties. To further support our proposals, we calculate the two sphere partition function of skew symplectic sigma models to determine geometric invariants, which confirm the anticipated Calabi–Yau threefold phases. We show that the two sphere partition functions of a pair of dual skew symplectic sigma models agree in a non-trivial fashion. To carry out these calculations, we develop a systematic approach to study higher-dimensional Mellin–Barnes type integrals. In particular, these techniques admit the evaluation of two sphere partition functions for gauged linear sigma models with higher rank gauge groups, but are applicable in other contexts as well. [ABSTRACT FROM AUTHOR]

Abstract: In arXiv:1008.1018 it is shown that a given stable vector bundle on a Calabi–Yau threefold which satisfies can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explicit examples of polystable bundles on elliptically fibered Calabi–Yau threefolds where it applies. The polystable bundle is given by a spectral cover bundle, for the visible sector, and a suitably chosen bundle, for the hidden sector. This provides a new class of heterotic flux compactifications via non-Kähler deformation of Calabi–Yau geometries with polystable bundles. As an application, we obtain examples of non-Kähler deformations of some three generation GUT models. [Copyright &y& Elsevier]

We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means. [ABSTRACT FROM AUTHOR]

We propose quantum states for Little String Theories (LSTs) arising from M5 branes probing A- and D-type singularities. This extends Witten's picture of M5 brane partition functions as theta functions to this more general setup. Compactifying the world-volume of the five-branes on a two-torus, we find that the corresponding theta functions are sections of line bundles over complex 4-tori. This formalism allows us to derive Seiberg-Witten curves for the resulting four-dimensional theories. Along the way, we prove a duality for LSTs observed by Iqbal, Hohenegger and Rey. [ABSTRACT FROM AUTHOR]

We give an elementary physical derivation of the Kontsevich-Soibelman wall crossing formula, valid for any theory with a 4d N = 2 supergravity description. Our argument leads to a slight generalization of the formula, which relates monodromy to the BPS spectrum., Physics

We investigate degeneracies of BPS states of D-branes on compact Calabi-Yau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial D-brane systems, and to clarify the subtle relation of Donaldson-Thomas invariants to BPS indices of stable D6-D2-D0 states, realized in supergravity as “hole halos.” We introduce a convergent generating function for D4 indices in the large CY volume limit, and prove it can be written as a modular average of its polar part, generalizing the fareytail expansion of the elliptic genus. We show polar states are “split” D6-anti-D6 bound states, and that the partition function factorizes accordingly, leading to a refined version of the OSV conjecture. This differs from the original conjecture in several aspects. In particular we obtain a nontrivial measure factor \(g^{−2}_{top} e^{−K}\) and find factorization requires a cutoff. We show that the main factor determining the cutoff and therefore the error is the existence of “swing states” — D6 states which exist at large radius but do not form stable D6-anti-D6 bound states. We point out a likely breakdown of the OSV conjecture at small \(g_{top}\) (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kähler moduli, a charge \(\Lambda \Gamma\) supporting single centered black holes of entropy \(\sim \Lambda^2 S(\Gamma)\) also admits two-centered BPS black hole realizations whose entropy grows like \(\Lambda^3\) when \(\Lambda \rightarrow \infty\)., Physics