Heterotic String Research Articles

Accelerating Kerr-Taub-NUT spacetime in the low energy limit of heterotic string theory

We construct a novel solution in the low energy limit of heterotic string theory describing accelerating charged and rotating black holes with NUT parameter. Some aspects of the new spacetime are discussed, such as locations of horizons, ergoregions, conic singularity, closed timelike curves, and area temperature product. We find some of the properties resemble the ones belong to accelerating Kerr-Newman-Taub-NUT spacetime.

Six-derivative Yang-Mills couplings in heterotic string theory

In this work, we present a comprehensive analysis of the structure of six-derivative bosonic couplings in heterotic string theory. First, we determine the maximal covariant and Yang-Mills gauge invariant basis, which consists of 801 independent coupling constants. By imposing T-duality constraints on the circular reduction of these terms, we obtain 468 relations between the coupling constants at the six-derivative order and the known couplings at lower derivative orders. Through the use of field redefinitions, we are able to eliminate the remaining 333 coupling constants. Remarkably, we find that the Yang-Mills field strength only appears through the trace of two field strengths or their derivatives. Finally, we perform further field redefinition to rewrite the remaining couplings in a canonical form characterized by 85 independent couplings.

Spinor–Vector Duality and Mirror Symmetry

Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened up a new field in pure mathematics, and was utilised in the area of enumerative geometry. Spinor–Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the Heterotic String, which includes the metric the antisymmetric tensor field and the Wilson line moduli. In terms of the toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas Spinor–Vector Duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of Spinor–Vector Duality in the effective field theory compactifications of string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited Spinor–Vector Duality and resolving the orbifold singularities, hence generating a smooth, effective field theory limit with an imprint of the Spinor–Vector Duality. Just like mirror symmetry, the Spinor–Vector Duality can be used to study the properties of complex manifolds with vector bundles. Spinor–Vector Duality offers a top-down approach to the “Swampland” program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not.

A twist at infinite distance in the CHL string

We analyze a space-time algebra of BPS states that emerges in the infinite distance limit in the moduli space of the nine-dimensional CHL string as the theory decompactifies to the ten-dimensional E8 × E8 heterotic string. We find an affine algebra as expected from the heterotic case, but in a twisted version.

Vanishing conditions for higher order couplings in heterotic theories

For compactifications of heterotic string theory, we elucidate simple cohomological conditions that lead to the vanishing of superpotential n-point couplings for all n. These results generalize some vanishing theorems for Yukawa couplings that have previously appeared in the literature to all higher orders. In some cases, these results are enough to show that certain fields do not appear in the perturbative superpotential at all. We illustrate our discussion with a number of concrete examples. In some cases, our results can be confirmed by showing that symmetries indeed forbid the couplings that vanish. In many, however, no such symmetries are known to exist and, as such, the infinite sets of vanishing couplings that are found are surprising from a four-dimensional perspective. Published by the American Physical Society 2024

The eclectic flavor symmetries of T2/ℤK\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbbm{T}}^2/{\\mathbb{Z}}_K $$\\end{document} orbifolds

Only four T2/ℤK\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbbm{T}}^2/{\\mathbb{Z}}_K $$\\end{document} orbifold building blocks are admissible in heterotic string compactifications. We investigate the flavor properties of all of these building blocks. In each case, we identify the traditional and modular flavor symmetries, and determine the corresponding representations and (fractional) modular weights of the available massless matter states. The resulting finite flavor symmetries include Abelian and non-Abelian traditional symmetries, discrete R symmetries, as well as the double-covered finite modular groups (S3 × S3) ⋊ ℤ4, T′, 2D3 and S3 × T′. Our findings provide restrictions for bottom-up model building with consistent ultraviolet embeddings.

O(9, 25) symmetry of heterotic string theory at orders α′, α′2

In a recent study, we have observed that by imposing a truncated T-duality transformation on the circular reduction of the bosonic couplings in the heterotic theory at four- and six-derivative orders, we can calculate these couplings in a particular YM gauge where the YM potential vanishes but its field strength remains non-zero. Importantly, the coupling constants are independent of the gauge choice, so these results are valid across different YM gauge choices.In this work, we explore the cosmological reduction of these couplings when the YM gauge fields belong to the Cartan subalgebra of SO(32) or E8 × E8. We demonstrate that after applying appropriate one-dimensional field redefinitions and total derivative terms, the couplings can be expressed in a proposed O(9, 25)-invariant canonical form, which is the extension of the canonical O(9, 9)-invariant form for just the NS-NS fields proposed by Hohm and Zwiebach. This O(9, 25)-invariant expression is in terms of the trace of the first time derivative of the generalized metric, which encompasses both the YM field and the NS-NS fields.

On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories

On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories

A T-duality of non-supersymmetric heterotic strings and an implication for Topological Modular Forms

Motivated by recent developments connecting non-supersymmetric heterotic string theory to the theory of Topological Modular Forms (TMF), we show that the worldsheet theory with central charge (17,32\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{3}{2} $$\\end{document}) obtained by fibering the (E8)1 × (E8)1 current algebra over the two 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} = (0, 1) sigma model on S1 with antiperiodic spin structure (such that the E8 factors are exchanged as we go around the circle), is continuously connected to the (E8)2 theory in the Gaiotto Johnson-Freyd Witten sense of going “up and down the RG trajectories”. Combined with the work of Tachikawa and Yamashita, this furnishes a physical derivation of the fact that the (E8)2 theory corresponds to the unique nontrivial torsion element [(E8)2] of TMF31 with zero mod-2 elliptic genus.

Gravitational index of the heterotic string

The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional 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 supergravity resolves the singularity. In doing so, we extend the recently-developed “new attractor mechanism” to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.

Brane profiles of non-supersymmetric strings

We connect the indications of 2D CFT for branes in non-supersymmetric strings to actual spacetime profiles, taking the bulk tadpole potentials into account. We find exact solutions for the uncharged branes that spread in the internal intervals of Dudas-Mourad vacua for non-tachyonic orientifolds and heterotic strings. These solutions involve suitable dressings of the uncharged branes of the nine-dimensional tadpole-free theory. Similar exact results for uncharged branes that are transverse to the internal space, or for charged branes, appear more challenging. Nevertheless, we identify their large-distance behavior, which is determined by linearized equations, and show that it is compatible with the CFT analysis in all expected cases. We also provide some hints on the leading back-reaction of the form-fields.

Modular forms and hierarchical Yukawa couplings in heterotic Calabi-Yau compactifications

We study the modular symmetry in heterotic string theory on Calabi-Yau threefolds. In particular, we examine whether moduli-dependent holomorphic Yukawa couplings are described by modular forms in the context of heterotic string theory with standard embedding. We find that SL(2, ℤ) modular symmetry emerges in asymptotic regions of the Calabi-Yau moduli space. The instanton-corrected holomorphic Yukawa couplings are then given by modular forms under SL(2, ℤ) or its congruence subgroups such as Γ0(3) and Γ0(4). In addition to the modular symmetry, it turns out that another coupling selection rule controls the structure of holomorphic Yukawa couplings. Furthermore, the coexistence of both the positive and negative modular weights for matter fields leads to a hierarchical structure of matter field Kähler metric. Thus, these holomorphic modular forms and the matter field Kähler metric play an important role in realizing a hierarchical structure of physical Yukawa couplings.

T-duality and flavor symmetries in Little String Theories

We explore the T-duality web of 6D Heterotic Little String Theories, focusing on flavor algebra reducing deformations. A careful analysis of the full flavor algebra, including Abelian factors, shows that the flavor rank is preserved under T-duality. This suggests a new T-duality invariant in addition to the Coulomb branch dimension and the two-group structure constants. We also engineer Little String Theories with non-simply laced flavor algebras, whose appearance we attribute to certain discrete 3-form fluxes in M-theory. Geometrically, these theories are engineered in F-theory with non-Kähler favorable K3 fibers. This geometric origin leads us to propose that freezing fluxes are preserved across T-duality. Along the way, we discuss various exotic models, including two inequivalent Spin(32)/ℤ2 models that are dual to the same E8 × E8 theory, and a family of self-T-dual models.

The frozen phase of heterotic F-theory duality

We study the duality between the Spin(32)/ℤ2 heterotic string without vector structure and F-theory with frozen singularities. We give a complete description in theories with 6d 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, 0) supersymmetry and identify the duals of Spin(32)/ℤ2-instantons on ADE singularities without vector structure in the frozen phase of F-theory using an ansatz introduced by Bhardwaj, Morrison, Tachikawa, and Tomasiello. As a consequence, we obtain a strongly coupled description of orbifold phases of type I string theory without vector structure, substantially expanding the list of known examples of 6d F-theory compactifications with frozen singularities. Supergravity theories can be fused from these instanton theories, in a way that commutes with switching off vector structure, which we use to propose new consistency checks via neutral hypermultiplet counting. Finally, we describe various Higgsings of this duality, and comment on constraints on higher form symmetries.

Self gravitating spinning string condensates

In the context of the black hole/string transition, it is useful to produce Euclidean string backgrounds representing hot and self-gravitating strings. We utilise analytical and numerical methods to find a smooth, stationary rotating solution in the heterotic string theory at high temperatures. The solution describes a spinning winding-momentum condensate living in three non-compact dimensions, and its backreaction on the thermal cycle. At low temperatures, we expect a transition between our solution to an analytical continuation of an axionic Kerr black hole.

Higgs branch of heterotic little string theories: Hasse diagrams and generalized symmetries

We study the Higgs branches of the 6D (1, 0) little string theories that live on the world volume of NS5-branes probing an ADE-singularity in the heterotic E8×E8 and Spin(32)/Z2 string theories. On the E8×E8 side, such little string theories (LSTs) are obtained via fusion of orbi-instanton SCFTs. For the C2/ZK orbifolds, we determine a magnetic quiver for the Higgs branch from the alternative type IIA brane system engineering the LST; we show that the magnetic quiver obtained in this way is the same as the Coulomb gauging of the 3D mirrors associated with the orbi-instanton building blocks. Using quiver subtraction, we determine the Hasse diagram of Higgs branch renormalization group flows between the LSTs, and we analyze how the structure constants of the generalized global symmetries vary along the edges of the Hasse diagram. From the Hasse diagram of the Higgs branch, we are immediately able to identify LSTs with the same T-duality-invariant properties, and thus propose candidate T-dual pairs. We perform a similar analysis of the Higgs branch Hasse diagram and putative T-dual families for particular E6-orbifold LSTs by taking advantage of a duality between a rank zero orbi-instanton theory and a rank one conformal matter theory. Published by the American Physical Society 2024

Extended doubled structures of algebroids for gauged double field theory

We study an analogue of the Drinfel’d double for algebroids associated with the O(D, D + n) gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three (twisted) Lie algebroids. They exhibit a “tripled”, which we call the extended double, rather than the “doubled” structure appearing in (ungauged) DFT. We find that the compatibilities of the extended doubled structure result not only in the strong constraint but also the additional condition in the gauged DFT. We establish a geometrical implementation of these structures in a (2D + n)-dimensional product manifold and examine the relations to the generalized geometry for heterotic string theories and non-Abelian gauge symmetries in DFT.

Four-derivative Yang-Mills couplings in heterotic theory through T-duality

This study delves into the dimensional reduction of the classical effective action of heterotic string theory on a circle, along with its T-duality symmetry, with the aim of identifying the bosonic couplings. To achieve this, we propose a truncation scheme for the generalized Buscher rules and the reduced action, specifically targeting the truncation of the nonlinear appearance of the scalar component of the Yang-Mills field in the base space. By imposing this truncated T-duality on the reduced action, we successfully determine the four- derivative bosonic couplings in the minimal basis, where field redefinition is imposed. Notably, these couplings, which are associated with the Lorentz Chern-Simons coupling HΩ, exhibit an exact correspondence with the NS-NS couplings found in the Metsaev-Tseytlin action.Furthermore, we investigate the bosonic couplings in the maximal basis, where field redefinition is not imposed. In this scenario, the truncated T-duality fixes the effective action up to 17 arbitrary parameters. By assigning specific values to these parameters, we establish a framework in which the NS-NS couplings align with those in the Meissner action. Remarkably, within this scheme, the Yang-Mills couplings precisely coincide with those obtained through the S-matrix method.

The minimal weak gravity conjecture

We examine the minimal constraints imposed by the Weak Gravity Conjecture (WGC) on the particle spectrum of a quantum gravity theory. Towers of super-extremal states have previously been argued to be required for consistency of the WGC under circle reduction. At the same time, there exist classes of theories where no tower of super-extremal particle states below the black hole threshold has been established with current techniques. We resolve this tension by arguing for the existence of a minimal radius for circle reductions of generic quantum gravity theories. Below this threshold, the notion of a circle compactification breaks down, bypassing the need for a tower of super-extremal states to satisfy the WGC after circle reduction. Based on this we propose that if a theory satisfies the WGC at the particle level below the black hole threshold, these states are sufficient for consistency under dimensional reduction, even in absence of a tower of super-extremal particles. Apart from general arguments, we provide independent evidence for this main result in F-, M- and string theory compactifications. According to the Emergent String Conjecture the only exception to the appearance of a minimal radius arises in asymptotically weak-coupling limits for heterotic strings, which aligns with the appearance of a weakly coupled super-extremal tower of particle states. This observation motivates a Minimal Weak Gravity Conjecture which states that towers of super-extremal particles occur if and only if they are required by consistency of the WGC under dimensional reduction.

Basis decompositions of genus-one string integrals

One-loop scattering amplitudes in string theories involve configuration-space integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein series in the integrand. A conjectural genus-one basis of integrands under Fay identities and integration by parts was recently constructed out of chains of Kronecker-Eisenstein series. In this work, we decompose a variety of more general genus-one integrands into the conjectural chain basis. The explicit form of the expansion coefficients is worked out for infinite families of cases where the Kronecker-Eisenstein series form cycles. Our results can be used to simplify multiparticle amplitudes in supersymmetric, heterotic and bosonic string theories and to investigate loop-level echoes of the field-theory double-copy structures of string tree-level amplitudes. The multitude of basis reductions in this work strongly validate the recently proposed chain basis and stimulate mathematical follow-up studies of more general configuration-space integrals with additional marked points or at higher genus.