arXiv subjects

Evgeny I. Buchbinder

Publications and source records attributed to Evgeny I. Buchbinder.

At least 19 recordsLinked to original sources

arXiv2026

Heat kernel approach to the one-loop effective action for nonlinear electrodynamics

We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the logarithmically divergent part of the effective action, the so-called induced action, corresponding to the DeWitt $a_2$ coefficient of the heat kernel. In NLED, quantisation yields non-minimal differential operators, for which standard heat kernel techniques are not immediately applicable. Considering the weak-field regime, we calculate the $a_0$, $a_1$ and $a_2$ contributions to leading order in the background electromagnetic field strength. Finally, we consider conformal NLED theories and compute the $a_0$ contribution to all orders. For this class, we comment on the role of causality being necessary and sufficient for the convergence of the exact $a_1$ and $a_2$ contributions.

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arXiv2026

Heterotic Flux Vacua with a Small Superpotential

We study heterotic Calabi--Yau compactifications with NSNS three-form flux in view of moduli stabilisation and investigate whether the value $|W_0|$ of the flux superpotential evaluated at supersymmetric minima can be small. Unlike in type IIB string theory, heterotic compactifications lack a no-scale structure, so that a non-vanishing flux superpotential generically induces a tree-level scalar potential for all moduli. Controlled moduli stabilisation therefore requires the flux superpotential to be sufficiently small in order to compete with non-perturbative effects. Working within a four-dimensional effective field theory and exploiting the special geometry of Calabi--Yau complex structure moduli spaces, we analyse the complex structure F-term equations and derive two no-go theorems: (1) supersymmetric vacua with vanishing $|W_0|$, which would lead to a vanishing tree-level scalar potential as in type IIB, occur only at singular loci in moduli space, and (2) no supersymmetric vacua with small $|W_0|$ exist in the large complex structure limit. Motivated by these results, we analyse explicit models away from the large complex structure regime using exact period expressions and identify one- and two-parameter examples in which suitable flux choices allow for values of $|W_0|$ of order unity, with some one-parameter models admitting values moderately below unity. Our findings show that small heterotic flux superpotentials are highly constrained, with the values of $|W_0|$ found in the examples studied being only marginally compatible with moduli stabilisation.

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arXiv2026

Gauge-invariant off-shell formulations for 3D massive higher-spin supermultiplets

Making use of the known off-shell formulations for massless higher-spin ${\cal N}=1$ supermultiplets in four dimensions, gauge-invariant off-shell actions for massive higher-spin ${\cal N}=2$ supermultiplets in three dimensions (3D) are derived by Kaluza-Klein reduction in superspace. To illustrate the formalism, we also construct, for the first time, massive gauge-invariant 3D ${\cal N}=2$ supersymmetric counterparts of the linearised actions for the old and new minimal supergravity theories. Our off-shell ${\cal N}=2$ supermultiplets carry a non-zero central charge, and are formulated in 3D ${\cal N}=2$ central charge superspace. The models can be reduced to 3D ${\cal N}=1$ superspace, by integrating out two Grassmann variables, and then consistent reality conditions on the superfields can be imposed. As a result, only two supercharges remain unbroken.

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arXiv2025

Massless higher-spin supermultiplets in 5D harmonic superspace

Off-shell actions for massless higher-spin $\mathcal{N}=1$ supermultiplets in five dimensions (5D) are constructed in harmonic superspace in terms of unconstrained prepotentials. Cubic couplings of these supermultiplets to the $q$-hypermultiplet are derived. We also provide a detailed derivation of the unconstrained prepotential for the 5D Weyl supermultiplet which has been used within the conformal superspace approach to $\mathcal{N}=1$ supergravity-matter systems.

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arXiv2024

Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins

We analyse the general structure of the three-point functions involving conserved higher-spin ``vector-like" supercurrents $J_{s}(z) := J_{α(s) \dotα(s)}(z)$ in four-dimensional $\mathcal{N}=1$ superconformal field theory. Using the constraints of superconformal symmetry and superfield conservation equations, we utilise a computational approach to analyse the general structure of the three-point function $\langle J^{}_{s_{1}}(z_{1}) \, J'_{s_{2}}(z_{2}) \, J''_{s_{3}}(z_{3}) \rangle$ and provide a general classification of the results. We demonstrate that the three-point function is fixed up to $2 \min (s_{i}) + 2$ independent conserved structures, which we propose to hold for arbitrary superspins. In addition, we show that the conserved structures can be classified as parity-even or parity-odd in superspace based on their transformation properties under superinversion.

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arXiv2023

Correlation functions of spinor current multiplets in ${\mathcal N}=1$ superconformal theory

We consider ${\mathcal N}=1$ superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet $S_α$ and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with ${\mathcal N}=2$ supersymmetry and contains the current of the second supersymmetry. However, we do not assume ${\mathcal N}=2$ supersymmetry. We show that the three-point function of two spinor current multiplets and the ${\mathcal N}=1$ supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the ${\mathcal N}=2$ supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in ${\mathcal N}=1$ superconformal field theory does not necessarily imply ${\mathcal N}=2$ superconformal symmetry.

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arXiv2023

Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins

We analyse the general structure of the three-point functions involving conserved higher-spin currents $J_{s} := J_{α(i) \dotα(j)}$ belonging to any Lorentz representation in four-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we computationally analyse the general structure of three-point functions $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$ for arbitrary spins and propose a classification of the results. For bosonic vector-like currents with $i=j$, it is known that the number of independent conserved structures is $2 \min (s_{i}) + 1$. For the three-point functions of conserved currents with arbitrarily many dotted and undotted indices, we show that in many cases the number of structures deviates from $2 \min (s_{i}) + 1$.

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arXiv2023

Three-point functions of fermionic higher-spin currents in 4D conformal field theory

We investigate the properties of a four-dimensional conformal field theory possessing a fermionic higher-spin current $Q_{α(2k) \dotα}$. Using a computational approach, we examine the number of independent tensor structures contained in the three-point correlation functions of two fermionic higher-spin currents with the conserved vector current $V_{m}$, and with the energy-momentum tensor $T_{m n}$. In particular, the $k = 1$ case corresponds to a "supersymmetry-like" current, that is, a fermionic conserved current with identical properties to the supersymmetry current which appears in $\mathcal{N} = 1$ superconformal field theories. However, we show that in general, the three-point correlation functions $\langle Q Q T\rangle $, $\langle \bar{Q} Q V\rangle $ and $\langle \bar{Q} Q T\rangle $ are not consistent with $\mathcal{N}=1$ supersymmetry

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arXiv2023

Grassmann-odd three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT

We consider the analytic construction of three-point functions of conserved higher-spin supercurrents in three-dimensional $\mathcal{N}=1$ superconformal field theory which are Grassmann-odd in superspace. In particular, these include the three-point functions of the supercurrent and flavour currents, which contain the three-point functions of the energy-momentum tensor and conserved vector currents at the component level. We present an analytic proof for arbitrary superspins that these correlators do not possess a parity-violating contribution. We also prove that the parity-even contribution is unique, and exists (under an assumption that is well supported by the computational approach of arXiv:2302.00593) for arbitrary superspins. The construction of the parity-even sector is shown to reduce to solving a system of linear homogeneous equations with a tri-diagonal matrix of co-rank one, which we solve explicitly for arbitrary superspins.

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arXiv2023

Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins

We analyse the general structure of the three-point functions of conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-point function $\langle \mathbf{J}^{}_{s_{1}} \mathbf{J}'_{s_{2}} \mathbf{J}''_{s_{3}} \rangle$, where $\mathbf{J}^{}_{s_{1}}$, $\mathbf{J}'_{s_{2}}$ and $\mathbf{J}''_{s_{3}}$ are conserved higher-spin supercurrents with superspins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). Using a computational approach limited only by computer power, we analytically impose the constraints arising from the superfield conservation equations and symmetries under permutations of superspace points. Explicit solutions for three-point functions are presented and we provide a complete classification of the results for $s_{i} \leq 20 $; the pattern is very clear, and we propose that our classification holds for arbitrary superspins. We demonstrate that Grassmann-even three-point functions are fixed up to one parity-even structure and one parity-odd structure, while Grassmann-odd three-point functions are fixed up to a single parity-even structure. The existence of the parity-odd structure in the Grassmann-even correlation functions is subject to a set of triangle inequalities in the superspins. For completeness, we also analyse the structure of three-point functions involving conserved higher-spin supercurrents and scalar superfields.

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arXiv2022

Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins

We analyse the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in three-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we use a computational formalism to analyse the general structure of $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$, where $J^{}_{s_{1}}$, $J'_{s_{2}}$ and $J''_{s_{3}}$ are conserved currents with spins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). The calculations are completely automated for any chosen spins and are limited only by computer power. We find that the correlation function is in general fixed up to two independent even structures, and one odd structure, subject to a set of triangle inequalities. We also analyse the structure of three-point functions involving higher-spin currents and fundamental scalars and spinors.

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arXiv2022

Three-point functions of higher-spin supercurrents in 4D ${\cal N}=1$ superconformal field theory

We develop a general formalism to study the three-point correlation functions of conserved higher-spin supercurrent multiplets $J_{α(r) \dotα(r)}$ in 4D ${\cal N}=1$ superconformal theory. All the constraints imposed by ${\cal N}=1$ superconformal symmetry on the three-point function $\langle J_{α(r_1) \dotα(r_1)} J_{β(r_2) \dotβ(r_2) }J_{γ(r_3) \dotγ(r_3)}\rangle$ are systematically derived for arbitrary $r_1, r_2, r_3$, thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in $\langle J_{α(r) \dotα(r)} J_{β\dotβ } J_{γ\dotγ}\rangle$, where $J_{α\dotα}$ is the supercurrent. We find that this three-point function depends on two independent tensor structures, though the precise form of the correlator depends on whether $r$ is even or odd. The case $r=1$ reproduces the three-point function of the ordinary supercurrent derived by Osborn. Additionally, we present the most general structure of mixed correlators of the form $\langle L L J_{α(r) \dotα(r)}\rangle$ and $\langle J_{α(r_1) \dotα(r_1)} J_{β(r_2) \dotβ(r_2)} L \rangle$, where $L$ is the flavour current multiplet.

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arXiv2021

Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory

We consider $\mathcal{N=1}$ superconformal field theories in three-dimensions possessing a conserved current multiplet $\mathcal{F}_{ (α_{1} α_{2} α_{3} α_{4}) }$ which we refer to as the superspin-2 current multiplet. At the component level it contains a conserved spin-2 current different from the energy-momentum tensor and a conserved fermionic higher spin current of spin 5/2. Using a superspace formulation, we calculate correlation functions involving $\mathcal{F}$, focusing particularly on the three-point function $ \langle \mathcal{F} \mathcal{F} \mathcal{F} \rangle $. After imposing the constraints arising from conservation equations and invariance under permutation of superspace points, we find that the parity-even and parity-odd sectors of this three-point function are each fixed up to a single coefficient. The presence of the parity-odd contribution is rather non-trivial, as there is an apparent tension between supersymmetry and the existence of parity-odd structures.

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arXiv2021

Three-point functions of higher-spin spinor current multiplets in ${\mathcal N}=1$ superconformal theory

In this paper, we study the general form of three-point functions of conserved current multiplets $S_{α(k)}= S_{(α_1 \dots α_k)}$ of arbitrary rank in four-dimensional ${\mathcal N}=1$ superconformal theory. We find that the correlation function of three such operators $\langle \bar{S}_{\dotα(k)} (z_1) S_{β(k+l)} (z_2) \bar{S}_{\dotγ(l)} (z_3) \rangle$ is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of $k$ and $l$. In addition, we present the general structure of mixed correlators of the form $\langle \bar{S}_{\dotα(k)} (z_1) S_{α(k)} (z_2) L(z_3) \rangle$ and $\langle \bar{S}_{\dotα(k)} (z_1) S_{α(k)} (z_2) J_{γ\dotγ} (z_3) \rangle$, where $L$ is the flavour current multiplet and $J_{γ\dotγ}$ is the supercurrent.

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arXiv2021

Mixed three-point functions of conserved currents in three-dimensional superconformal field theory

We consider mixed three-point correlation functions of the supercurrent and flavour current in three-dimensional $1 \leq \mathcal{N} \leq 4$ superconformal field theories. Our method is based on the decomposition of the relevant tensors into irreducible components to guarantee that all possible tensor structures are systematically taken into account. We show that only parity even structures appear in the correlation functions. In addition to the previous results obtained in arXiv:1503.04961, it follows that supersymmetry forbids parity odd structures in three-point functions involving the supercurrent and flavour current multiplets.

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arXiv2019

Instantons and Hilbert Functions

We study superpotentials from worldsheet instantons in heterotic Calabi-Yau compactifications for vector bundles constructed from line bundle sums, monads and extensions. Within a certain class of manifolds and for certain second homology classes, we derive simple necessary conditions for a non-vanishing instanton superpotential. These show that non-vanishing instanton superpotentials are rare and require a specific pattern for the bundle construction. For the class of monad and extension bundles with this pattern, we derive a sufficient criterion for non-vanishing instanton superpotentials based on an affine Hilbert function. This criterion shows that a non-zero instanton superpotential is common within this class. The criterion can be checked using commutative algebra methods only and depends on the topological data defining the Calabi-Yau X and the vector bundle V.

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arXiv2019

Heterotic Instantons for Monad and Extension Bundles

We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field axion inflation, which makes their presence or absence, as well as their functional dependence on moduli, an important issue. We develop geometric methods to compute the instanton superpotentials for heterotic string theory with monad and extension bundles. Using our methods, we find a variety of examples with a non-vanishing superpotential. In view of standard vanishing theorems, we speculate that these results are likely to be attributed to the non-compactness of the instanton moduli space. We test this proposal, for the case of monad bundles, by considering gauged linear sigma models where compactness of the instanton moduli space can be explicitly checked. In all such cases, we find that the geometric results are consistent with the vanishing theorems. Surprisingly, linearly dependent Pfaffians even arise for cases with a non-compact instanton moduli space. This suggests some gauged linear sigma models with a non-compact instanton moduli space may still have a vanishing instanton superpotential.

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arXiv2019

Linearised actions for $\cal N$-extended (higher-spin) superconformal gravity

The off-shell actions for $\cal N$-extended conformal supergravity theories in three dimensions were formulated in [1,2] for $1\leq {\cal N} \leq 6$ using a universal approach. Each action is generated by a closed super three-form which is constructed in terms of the constrained geometry of $\cal N$-extended conformal superspace. In this paper we initiate a program to recast these actions (and to formulate their higher-spin counterparts) in terms of unconstrained gauge prepotentials as integrals over the full superspace. We derive transverse projection operators in $\cal N$-extended Minkowski superspace and then use them to construct linearised rank-$n$ super-Cotton tensors and off-shell $\cal N$-extended superconformal actions. We also propose off-shell gauge-invariant actions to describe massive higher-spin supermultiplets in $\cal N$-extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in $\cal N$-extended supersymmetry.

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