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Eirik Eik Svanes

Publications and source records attributed to Eirik Eik Svanes.

At least 19 recordsLinked to original sources
arXiv2026

On a Deformed Holomorphic Chern-Simons Theory

We deform classical holomorphic Chern--Simons theory on a Calabi--Yau three-fold $X$ by deforming the complex structure by a deformation parameter $h \in\mathscr{H}^{0,1}(T^{1,0}X)$. The corresponding equations of motion admit new "instanton solutions" which which are invariant under re-scalings of $h$, and are perhaps more reminiscent of $G_2$-instantons for $G_2$ manifolds. We give examples of such instantons. In particular, when $h$ has non-vanishing Yukawa coupling ${\rm Yuk}(h,h,h)\neq 0$, it may be used to define a connection on ${\rm End}(T^{1,0}X)$ solving the instanton constraint. Interestingly, this connection gives rise to a hermitian (self-adjoint) connection for a real gauge theory on the real bundle ${\rm End}(TX)$ for only specific directions in deformation space, which may be classified using Morse theory. We quantize the deformed theory around these instanton backgrounds, and derive explicit expressions for the partition function in the limit where the complex structure deformation is large. We study anomalies, and the $h$-dependece of the partition function. In particular, coupling the theory to additional gravitational degrees of freedom, we find that the special directions in deformation space give rise to novel anomaly free theories on ${\rm End}(T^{1,0}X)$.

hep-th↗
arXiv2026

Holomorphic supergravity in ten dimensions and anomaly cancellation

We formulate a ten-dimensional version of Kodaira-Spencer gravity on a Calabi-Yau five-fold that reproduces the classical Maurer-Cartan equation governing supersymmetric heterotic moduli. Quantising this theory's quadratic fluctuations, we show that its one-loop partition function simplifies to products of holomorphic Ray-Singer torsions and exhibits an anomaly that factorises as in $SO(32)$ and $E_8\times E_8$ supergravity. Based on this, we conjecture that this theory is the $SU(5)$-twisted version of ten-dimensional $N=1$ supergravity coupled to Yang-Mills and show that is related to the type I Kodaira-Spencer theory of Costello-Li via a non-local field redefinition. The counter-terms needed to cancel the anomaly and retain gauge invariance for the one-loop effective theory reconstruct the differential of a recently discovered double-extension complex. This complex has non-tensorial extension classes and its first cohomology counts the infinitesimal moduli of heterotic compactifications modulo order $α'^2$ corrections.

hep-th↗
arXiv2025

Local descriptions of the heterotic SU(3) moduli space

The heterotic $SU(3)$ system, also known as the Hull--Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system on a compact 6-manifold $X$, using a vector bundle $Q=(T^{1,0}X)^* \oplus {End}(E) \oplus T^{1,0}X$, where $E\to X$ is the classical gauge bundle arising in the system. We establish that the moduli space has an expected dimension of zero. We achieve this by studying the deformation complex associated to a differential operator $\bar{D}$, which emulates a holomorphic structure on $Q$, and demonstrating an isomorphism between the two cohomology groups which govern the infinitesimal deformations and obstructions in the deformation theory for the system. We also provide a Dolbeault-type theorem linking these cohomology groups to Čech cohomology, a result which might be of independent interest, as well as potentially valuable for future research.

math.DG↗
arXiv2025

The heterotic $G_2$ moduli space metric

In this article we dimensionally reduce a heterotic supergravity on a $G_2$ background with Minkowski spacetime using a certain cohomology as a basis for the Kaluza-Klein expansion, up to and including first order in $α'$. We construct the moduli space heterotic $G_2$ compactifications. The $α'$-correction induces a curvature correction to the Weyl-Peterson metric. In the limit in which the $G_2$ manifold reduces to $SU(3)$, we recover known results.

hep-th↗
arXiv2025

The physical moduli of heterotic G_2 string compactifications

In previous works, an operator was developed for heterotic compactifications on $\mathbb{R}^{2,1}\times G_2$ and $AdS_3 \times G_2$, which preserves $N=1$ $d=3$ supersymmetry and whose kernel is related to the moduli of the compactification. The operator is described in terms of non-physical spurious degrees of freedom, specifically, deformations of a connection on the tangent bundle. In this paper, we eliminate these spurious degrees of freedom by linking deformations of the spin connection to the moduli of the $G_2$ manifold $Y$. This results in an operator $\check D$ that captures the physical moduli space of the $G_2$ heterotic string theory. When $Y=X\times S^1$, with $X$ an $SU(3)$ manifold, we show $\check D$ produces results that align with existing literature. This allows us to propose a $G_2$ moduli space metric. We check that this metric reduces to the $SU(3)$ moduli metric constructed in the literature. We then define an adjoint operator ${\check D}^†$. We show the $G_2$ moduli correspond to the intersection of the kernels of $\check D$ and ${\check D}^†$. These kernels reduce to the $SU(3)$ F-terms and D-terms respectively on $X\times S^1$. This gives two non-trivial consistency checks of our proposed moduli space metric. Working perturbatively in $α'$, we also demonstrate that the heterotic $G_2$ moduli problem can be characterised in terms of a double extension of ordinary bundles, just like in the $SU(3)$ case.

hep-th↗
arXiv2025

A Heterotic Kähler Gravity and the Distance Conjecture

Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the complex structure deformations (the Beltrami differential). Treated separately, for large fluxes, or alternatively at large distances in the background complex structure moduli space, these fields can be integrated out to obtain a new field theory in the remaining fields, which describe the complexified hermitian and gauge degrees of freedom. We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. In the process, we define a new type of symplectic cohomology theory, where the background complex structure Beltrami differential plays the role of the symplectic form.

hep-th↗
arXiv2024

The moduli of the universal geometry of heterotic moduli

We study the moduli of the universal geometry of $d=4$ $N=1$ heterotic vacua. Universal geometry refers to a family of heterotic vacua fibered over the moduli space. The universal geometry mimics aspects of the original heterotic vacua, in particular holomorphic data such as F-terms, as well as the Green-Schwarz Bianchi identity. Here we study first order deformations of the universal geometry and find this provides a shortcut to computing second order deformations of the original problem. The equations governing the moduli of the universal geometry are remarkably similar to the equations of the underlying heterotic theory and we find a fascinating double extension structure that mirrors the original heterotic problem. As an application we find first order universal deformations determine second order deformations of the original heterotic theory. This gives a shortcut to determining results that are otherwise algebraically unwieldy. The role of the D-terms is closely related to the existence of flat connections on the moduli space. Finally, we re-derive some of these results by direct differentiation - this direct approach requires significantly more calculation.

hep-th↗
arXiv2024

Recent Developments in Heterotic Moduli

We review recent results for heterotic moduli and the Hull--Strominger system. In particular, we discuss mathematical properties of the recently derived deformation operator $\bar D$ associated to the deformation complex of heterotic $SU(3)$ solutions. We review results on Serre duality, showing that the operator has a vanishing index, and discuss a notion of Čech cohomology and a particular instance of a Dolbeault theorem for $\bar D$. Specifically, the cohomology parametrising infinitesimal deformations is isomorphic to the first Čech cohomology of an associated cochain complex. This will be useful for future research, as it provides a more algebraic handle on the heterotic moduli problem, which is useful for understanding notions of stability, geometric invariants, and enumerative geometry for the Hull--Strominger system.

hep-th↗
arXiv2024

The decoupling of moduli about the standard embedding

We study the cohomology of an elliptic differential complex arising from the infinitesimal moduli of heterotic string theory. We compute these cohomology groups at the standard embedding, and show that they decompose into a direct sum of cohomologies. While this is often assumed in the literature, it had not been explicitly demonstrated. Given a stable gauge bundle over a complex threefold with trivial canonical bundle and no holomorphic vector fields, we also show that the Euler characteristic of this differential complex is zero. This points towards a perfect obstruction theory for the heterotic moduli problem, at least for the most physically relevant compactifications.

hep-th↗
arXiv2024

BPS complexes and Chern--Simons theories from $G$-structures in gauge theory and gravity

We consider a variety of physical systems in which one has states that can be thought of as generalised instantons. These include Yang--Mills theories on manifolds with a torsion-free $G$-structure, analogous gravitational instantons and certain supersymmetric solutions of ten-dimensional supergravity, using their formulation as generalised $G$-structures on Courant algebroids. We provide a universal algebraic construction of a complex, which we call the BPS complex, that computes the infinitesimal moduli space of the instanton as one of its cohomologies. We call a class of these spinor type complexes, which are closely connected to supersymmetric systems, and show how their Laplacians have nice properties. In the supergravity context, the BPS complex becomes a double complex, in a way that corresponds to the left- and right-moving sectors of the string, and becomes much like the double complex of $(p,q)$-forms on a Kähler manifold. If the BPS complex has a symplectic inner product, one can write down an associated linearised BV Chern--Simons theory, which reproduces several classic examples in gauge theory. We discuss applications to (quasi-)topological string theories and heterotic superpotential functionals, whose quadratic parts can also be constructed naturally from the BPS complex.

hep-th↗
arXiv2024

A Heterotic Hermitian--Yang--Mills Equivalence

We consider N=1, d=4 vacua of heterotic theories in the large radius limit in which alpha' << 1. We construct a real differential operator $\mathcal{D}= D+\bar{D}$ on an extension bundle $(Q, \mathcal{D})$ with underlying topology $Q=(T^{1,0}X)^* \oplus {\rm End} \, E \oplus T^{1,0} X$ whose curvature is holomorphic and Hermitian-Yang-Mills with respect to the complex structure and metric on the underlying non-Kahler complex 3-fold X if and only if the heterotic supersymmetry equations and Bianchi identity are satisfied. This is suggestive of an analogue of the Donaldson--Uhlenbeck--Yau correspondence for heterotic vacua of this type.

hep-th↗
arXiv2023

1PN effective binary Lagrangian for the gravity-Kalb-Ramond sector in the conservative regime

Within the framework of string theory, a number of new fields are possible correcting the Einstein-Hilbert action, including a Kalb-Ramond two-form field. In this work we derive explicitly first order relativistic corrections to conservative dynamics with a Kalb-Ramond field, using the effective field theory approach. The resulting additional terms in the Lagrangian governing conservative binary dynamics are presented explicitly.

gr-qc↗
arXiv2023

A heterotic Kodaira-Spencer theory at one-loop

We consider a heterotic version of six-dimensional Kodaira-Spencer gravity derived from the heterotic superpotential. We compute the one-loop partition function and find it can be expressed as a product of holomorphic Ray-Singer torsions. We discuss its topological properties and potential gauge and gravitational anomalies. We show these anomalies can be cancelled using Green-Schwarz-like counter-terms. We also discuss the dependence on the background geometry, and in particular the choice of hermitian metric needed for quantisation. Given suitable topological constraints, this dependence may again be cancelled by the addition of purely background-dependent counter-terms. We also explain how our methods provide the one-loop partition functions of a large class of more general holomorphic field theories in terms of holomorphic Ray-Singer torsions.

hep-th↗
arXiv2022

Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions

We study the gauging of a discrete $\mathbb{Z}_3$ symmetry in the five-dimensional superconformal $T_N$ theories. We argue that this leads to an infinite sequence of five-dimensional superconformal theories with either $E_6 \times SU(N)$ or $SU(3)\times SU(N)$ global symmetry group. In the $M$-theory realisation of $T_N$ theories as residing at the origin in the Calabi-Yau orbifolds ${\mathbb{C}^3 \over {\mathbb{Z}_N \times \mathbb{Z}_N}}$ we identify the $\mathbb{Z}_3$ symmetry geometrically and the new theories arise from $M$-theory on the non-Abelian orbifolds $({\mathbb{C}^3 \over {\mathbb{Z}_N \times \mathbb{Z}_N}})/{\mathbb{Z}_3}$. On the other hand, in the $(p,q)$ 5-brane web description in Type IIB theory, the symmetry combines the $U$-duality symmetry with a rotation in space, defining a so-called $U$-fold background, where the $E_6$ symmetry is manifest.

hep-th↗
arXiv2021

Heterotic Quantum Cohomology

We reexamine the massless spectrum of a heterotic string vacuum at large radius and present two results. The first result is to construct a vector bundle $\mathcal{Q}$ and operator $\overline{\mathcal{D}}$ whose kernel amounts to deformations solving `F-term' type equations. This resolves a dilemma in previous works in which the spin connection is treated as an independent degree of freedom, something that is not the case in string theory. The second result is to utilise the moduli space metric, constructed in previous work, to define an adjoint operator $\overline{\mathcal{D}}^†$. The kernel of $\overline{\mathcal{D}}^†$ amounts to deformations solving `D-term' type equations. Put together, we show there is a vector bundle $\mathcal{Q}$ with a metric, a $\overline{\mathcal{D}}$ operator and a gauge fixing (holomorphic gauge) in which the massless spectrum are harmonic representatives of $\overline{\mathcal{D}}$. This is remarkable as previous work indicated the Hodge decomposition of massless deformations were complicated and in particular not harmonic except at the standard embedding.

hep-th↗
arXiv2021

Topological G$_{2}$ and Spin(7) strings at 1-loop from double complexes

We study the topological $G_2$ 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 $G_2$ 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.

hep-th↗
arXiv2020

New $G_2$-conifolds in $M$-theory and their Field Theory Interpretation

A recent theorem of Foscolo-Haskins-Nordström which constructs complete $G_2$-holonomy orbifolds from circle bundles over Calabi-Yau cones can be utilised to construct and investigate a large class of generalisations of the $M$-theory flop transition. We see that in many cases a UV perturbative gauge theory appears to have an infrared dual described by a smooth $G_2$-holonomy background in $M$-theory. Various physical checks of this proposal are carried out affirmatively.

hep-th↗