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A. A. Tseytlin

Publications and source records attributed to A. A. Tseytlin.

At least 19 recordsLinked to original sources
arXiv2026

M2 brane in AdS$_4\times S^7/\mathbb Z_k$: 2-loop correction to $\frac{1}{2}$-BPS Wilson loop vs localization in ABJM theory

We study the quantization of an M2 brane wrapping $\mathrm{AdS}_2\times S^1$ inside $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$, dual to the $\frac{1}{2}$-BPS circular Wilson loop in ABJM theory. The classical action and the one-loop contribution were previously shown to reproduce the gauge-theory localization result. Here we extend the analysis to the two-loop order. In an adapted static and $κ$-symmetry gauge the world-volume action contains no cubic interaction vertices, so that the two-loop correction is determined entirely by quartic interactions and is manifestly free of logarithmic UV divergences. We find that the bosonic and fermionic contributions combine into a perfect square $ {\mathscr X}^2$ where ${\mathscr X}$ is a linear combination of the bosonic and fermionic 3d Green's functions and their derivatives. The evaluation of $\mathscr X$ requires fixing the $\mathrm{AdS}_2$ boundary quantization of the massless fermionic modes. With the boundary conditions selected by the preserved supersymmetry, $\mathscr X$ vanishes and hence the complete two-loop correction is found to be zero. This result would not be consistent with identifying the M2-brane loop expansion directly with the large-$N$ expansion of the canonical, fixed-$(N,k)$ localization prediction. Instead, it agrees precisely with the recent proposal that the semiclassical M2-brane partition function should be matched to the gauge-theory grand-canonical ensemble, in which the Wilson loop expectation value is perturbatively one-loop exact. The vanishing of the two-loop correction thus provides a non-trivial test of this grand-canonical identification.

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arXiv2026

Duality and Dilaton

We review and elaborate on the issue of the dilaton transformation under the usual $r \rightarrow α'/r$ target space duality and its non-static generalization (or $σ$-model duality). It is found that the transformation law $r \rightarrow α'/r$, $ϕ\rightarrow ϕ- \ln(r/\sqrt{α'})$ which guarantees duality at the one-loop $σ$-model level should be modified at two (and higher) loop order. The non-static duality is illustrated on the example of cosmological solutions in $D \ge 2$ with time-dependent radii of space torus.

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arXiv2025

2-loop scattering on superstring and supermembrane in flat space

We consider the S-matrix of transverse scalar excitations on an infinite $D=10$ GS superstring and $D=11$ supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the $D=10$ GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.

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arXiv2024

Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations

We consider the ABF background underlying the eta-deformed AdS5 x S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still correspond to UV finite theory on a flat 2d world-sheet, implying that the eta-deformed model is scale invariant. This property follows from the formal relation via T-duality between the eta-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R-R field strengths are of the second order in derivatives. Surprisingly, we also find that the this background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R-R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after the T-duality, to a modification of type II equations from their standard form. We conjecture that the modified equations should follow from kappa-symmetry of the eta-deformed model. All our observations apply also to eta-deformations of AdS3 x S3 and AdS2 x S2 models.

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arXiv2023

Exact strong coupling results in $\cal N$=2 $Sp(2N)$ superconformal gauge theory from localization

We apply the localization technique to compute the free energy on four-sphere and the circular BPS Wilson loop in the four-dimensional $\cal N$=2 superconformal $Sp(2N)$ gauge theory containing vector multiplet coupled to four hypermultiplets in fundamental representation and one hypermultiplet in rank-2 antisymmetric representation. This theory is unique among similar $\cal N$=2 superconformal models that are planar-equivalent to $\cal N$=4 SYM in that the corresponding localization matrix model has the interaction potential containing single-trace terms only. We exploit this property to show that, to any order in large $N$ expansion and an arbitrary 't Hooft coupling $λ$, the free energy and the Wilson loop satisfy Toda lattice equations. Solving these equations at strong coupling, we find remarkably simple expressions for these observables which include all corrections in $1/N$ and $1/\sqrtλ$. We also compute the leading exponentially suppressed ${\cal O}(e^{-\sqrtλ})$ corrections and consider a generalization to the case when the fundamental hypermultiplets have a non-zero mass. The string theory dual of this $\cal N$=2 gauge theory should be a particular orientifold of AdS$_5 \times S^5$ type IIB string and we discuss the string theory interpretation of the obtained strong-coupling results.

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arXiv2023

Non-planar corrections in orbifold/orientifold $\mathcal N=2$ superconformal theories from localization

We study non-planar corrections in two special $\mathcal N=2$ superconformal $SU(N)$ gauge theories that are planar-equivalent to $\mathcal N=4$ SYM theory: two-nodes quiver model with equal couplings and $\mathcal N=2$ vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. We focus on two observables in these theories that admit representation in terms of localization matrix model: free energy on 4-sphere and the expectation value of half-BPS circular Wilson loop. We extend the methods developed in arXiv:2207.11475 to derive a systematical expansion of non-planar corrections to these observables at strong 't Hooft coupling constant $λ$. We show that the leading non planar corrections are given by a power series in $λ^{3/2}/N^2$ with rational coefficients. Sending $N$ and the coupling constant $λ$ to infinity with $λ^{3/2}/N^2$ kept fixed corresponds to the familiar double scaling limit in matrix models. We find that in this limit the observables in the two models are related in a remarkably simple way: the free energies differ by the factor of $2$, whereas the Wilson loop expectation values coincide. Surprisingly, these relations hold only at strong coupling, they are not valid in the weak coupling regime. We also discuss a dual string theory interpretation of the leading corrections to the free energy in the double scaling limit suggesting their relation to curvature corrections in type IIB string effective action.

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arXiv2023

Strong coupling expansion in $\mathbf{\mathcal N=2}$ superconformal theories and the Bessel kernel

We consider strong 't Hooft coupling expansion in special four-dimensional $\mathcal N=2$ superconformal models that are planar-equivalent to $\mathcal N=4$ super Yang-Mills theory. Various observables in these models that admit localization matrix model representation can be expressed at large $N$ in terms of a Fredholm determinant of a Bessel operator. The latter previously appeared in the study of level spacing distributions in matrix models and, more recently, in four-point correlation functions of infinitely heavy half-BPS operators in planar $\mathcal N=4$ SYM. We use this relation and a suitably generalized Szego-Akhiezer-Kac formula to derive the strong 't Hooft coupling expansion of the leading corrections to free energy, half-BPS circular Wilson loop, and certain correlators of chiral primaries operators in the $\mathcal N=2$ models. This substantially generalizes partial results in the literature and represents a challenge for dual string theory calculations in AdS/CFT context. We also demonstrate that the resulting strong-coupling expansions suffer from Borel singularities and require adding non-perturbative, exponentially suppressed corrections. As a byproduct of our analysis, we determine the non-perturbative correction to the above mentioned four-point correlator in planar $\mathcal N=4$ SYM.

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arXiv2023

Comments on 4-derivative scalar theory in 4 dimensions

We review and elaborate on some aspects of the classically scale-invariant renormalizable 4-derivative scalar theory $L= ϕ\, \partial^4 ϕ+ g (\partial ϕ)^4$. Similar models appear, e.g., in the context of conformal supergravity or in the description of the crystalline phase of membranes. Considering this theory in Minkowski signature we suggest how to define Poincare-invariant scattering amplitudes by assuming that only massless oscillating (non-growing) modes appear as external states. In such shift-symmetric interacting theory there are no IR divergences despite the presence of $1/q^4$ internal propagators. We discuss how non-unitarity of this theory manifests itself at the level of the one-loop massless scattering amplitude.

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arXiv2022

On type IIB supergravity action on $M^5 \times X^5$ solutions

While the 10d type IIB supergravity action evaluated on AdS$_5\times S^5$ solution vanishes, the 5d effective action reconstructed from the equations of motion using $M^5 \times S^5$ compactification ansatz is proportional to the AdS$_5$ volume. The latter is consistent with the conformal anomaly interpretation in AdS/CFT context. We show that this paradox can be resolved if, in the case of $M^5 \times X^5$ topology, the 10d action contains an additional 5-form dependent "topological" term $\int F_{5M} \wedge F_{5X}$. The presence of this term is suggested also by gauge-invariance considerations in the PST formulation of type IIB supergravity action. We show that this term contributes to the 10d action evaluated on the D3-brane solution.

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arXiv2022

Strong coupling expansion of free energy and BPS Wilson loop in $\mathcal N=2$ superconformal models with fundamental hypermultiplets

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $\mathcal N=2$ 4d superconformal models we consider two special theories with gauge groups $SU(N)$ and $Sp(2N)$. They contain $N$-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $\mathcal N=4$ SYM theories. These $\mathcal N=2$ theories can be realised on a system of $N$ D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of $AdS_5\times S^5$ superstring. Starting with the localization matrix model representation for the $\mathcal N=2$ partition function on $S^4$ we find exact differential relations between the $1/N$ terms in the corresponding free energy $F$ and the $\frac{1}{2}$-BPS Wilson loop expectation value $\langle\mathcal W\rangle$ and also compute their large 't Hooft coupling ($λ\gg 1$) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable $Sp(2N)$ case we find an exact resummed expression for the leading strong coupling terms at each order in the $1/N$ expansion. We also determine the exponentially suppressed at large $λ$ contributions to the non-planar corrections to $F$ and $\langle\mathcal W\rangle$ and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

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arXiv2020

Quantum strings in AdS5 x S5 and AdS/CFT duality

We review some recent progress in understanding the spectrum of energies/dimensions of strings/operators in AdS5 x S5 -- planar N=4 super Yang-Mills correspondence. We consider leading strong coupling corrections to the energy of lightest massive string modes in AdS5 x S5, which should be dual to members of the Konishi operator multiplet in the SYM theory. This determines the general structure of strong-coupling expansion of the anomalous dimension of the Konishi operator. Following arXiv:0906.4294 we use 1-loop results for semiclassical string states to extract information about the leading coefficients in this expansion.

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arXiv2020

Comments on open string with "massive" boundary term

We make some remarks on possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the 1d metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

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arXiv2018

Scalar scattering via conformal higher spin exchange

Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved currents) with conformal higher spin fields in flat space. We compute the tree-level four-scalar scattering amplitude using a natural prescription for summation over an infinite set of conformal higher spin exchanges and find that it vanishes (modulo delta-function terms having support on measure-zero domain in phase space). Independently, we show that this vanishing of the scalar scattering amplitude is, in fact, implied by the global conformal higher spin symmetry of this model. We also discuss one-loop corrections to the four-scalar scattering amplitude.

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arXiv2018

On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix

We consider superstring theory on AdS_3 x S^3 x T^4 supported by a combination of RR and NSNS 3-form fluxes (with parameter of the NSNS 3-form q). This theory interpolates between the pure RR flux model (q=0) whose spectrum is expected to be described by a Bethe ansatz and the pure NSNS flux model (q=1) which is described by the supersymmetric extension of the SL(2,R) x SU(2) WZW model. As a first step towards the solution of this integrable theory for generic value of q we compute the corresponding tree-level S-matrix for massive BMN-type excitations. We find that this S-matrix has a surprisingly simple dependence on q: the diagonal amplitudes have exactly the same structure as in the q=0 case but with the BMN dispersion relation e^2 = p^2 + 1 replaced by the one with shifted momentum and mass, e^2 = (p + q)^2 + 1 - q^2. The off-diagonal amplitudes are then determined from the classical Yang-Baxter equation. We also construct the Pohlmeyer reduced model corresponding to this superstring theory and find that it depends on q only through its mass-squared parameter proportional to (1-q^2), implying that its relativistic S-matrix is q-independent.

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arXiv2017

On induced action for conformal higher spins in curved background

We continue the investigation of the structure of the action for a tower of conformal higher spin fields in non-trivial 4d background metric recently discussed in arXiv:1609.09381. The action is defined as an induced one from path integral of a conformal scalar field in curved background coupled to higher spin fields. We analyse in detail the dependence of the quadratic part of the induced action on the spin 1 and spin 3 fields, determining the presence of a curvature-dependent mixed spin 1 - spin 3 term. One consequence is that the pure spin 3 kinetic term cannot be gauge-invariant on its own beyond the leading term in small curvature expansion. We also compute the non-zero contribution of the 1-3 mixing term to the conformal anomaly c-coefficient. One is thus to determine all such mixing terms before addressing the question of possible vanishing of the total c-coefficient in the conformal higher spin theory.

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arXiv2017

On divergences in non-minimal N=4 conformal supergravity

We review the question of quantum consistency of N=4 conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ("minimal") conformal supergravity where the complex scalar $ϕ$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to N=4 super Yang-Mills with gauge group of dimension 4. The same turns out to be true also for the "non-minimal" N=4 conformal supergravity with the action (recently constructed in arXiv:1609.09083) depending on an arbitrary holomorphic function $f(ϕ)$. The special case of the "non-minimal" conformal supergravity with $f= e^{2ϕ}$ appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function $f$ and thus can be cancelled just as in the "minimal" $f=1$ case by coupling the theory to four N=4 vector multiplets.

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arXiv2017

Partition function of free conformal fields in 3-plet representation

Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher spins in AdS_{d+1}. One may also study generalizations when conformal fields belong to higher dimensional representations, i.e. carry more than two internal symmetry indices. Here we consider the case of the 3-fundamental ("3-plet") representation. One motivation is a conjectured connection to multiple M5-brane theory: heuristic arguments suggest that it may be related to an (interacting) CFT of 6d (2,0) tensor multiplets in 3-plet representation of large N symmetry group that has an AdS_7 dual. We compute the singlet partition function Z on S^1 x S^{d-1} for a free field in 3-plet representation of U(N) and analyse its novel large N behaviour. The large N limit of the low temperature expansion of Z which is convergent in the vector and adjoint cases here is only asymptotic, reflecting the much faster growth of the number of singlet operators with dimension, indicating a phase transition at very low temperature. Indeed, while the critical temperatures in the vector (T_c ~ N^a, a >0) and adjoint (T_c ~ 1) cases are finite, we find that in the 3-plet case T_c ~ 1/ log N, i.e. it approaches zero at large N. We discuss some details of large N solution for the eigenvalue distribution. Similar conclusions apply to higher p-plet representations of U(N) or O(N) and also to the free p-tensor theories invariant under [U(N)]^p or [O(N)]^p starting with p=3.

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