arXiv subjects

Arkady A. Tseytlin

Publications and source records attributed to Arkady A. Tseytlin.

At least 19 recordsLinked to original sources

arXiv2026

M2 brane $S^3/\mathbb Z_k$ instanton partition function in ${\rm AdS}_4\times S^7/\mathbb Z_k$: 2-loop correction

As was shown in arXiv:2609.14497, the 2-loop correction to the partition function of M2 brane wrapping $\mathrm{AdS}_2\times S^1$ inside $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$ vanishes, in agreement with the localization prediction for $\frac{1}{2}$-BPS Wilson loop in ABJM theory in the grand-canonical ensemble according to the conjecture of arXiv:2505.21633. Here we study the 2-loop correction in the case of the M2 brane instanton $S^3/\mathbb Z_k\subset S^7/\mathbb Z_k$ dual to non-perturbative large $N$ contribution to ABJM free energy on 3-sphere. The 1-loop instanton contribution was shown in arXiv:2307.14112 to match the localization prediction. The 2-loop computation is complicated by the presence of bosonic and fermionic zero modes, which require using projected Green's functions and accounting for the collective-coordinate Jacobian. The Jacobian provides a non-trivial 2-loop contribution in addition to the one of the 4-vertex in the M2 brane action. We find that for $k>2$ the transcendental $k$-dependence of the 4-vertex contribution is cancelled by the Jacobian for any choice of the separation of the fermionic zero modes from the quantum fields. The residual rational term vanishes for the separation selected by the supersymmetry, under which the collective coordinates and the quantum fields form separate supermultiplets. We conjecture that the remaining integral over the collective coordinates contributes only to an overall normalization of the partition function, so it is 1-loop exact. For $k=1$ the quartic vertex contribution reduces to equation-of-motion terms as in the case of ${\rm AdS}_3 \subset { \rm AdS}_7 \times S^4$ in arXiv:2511.22306 related to $S^3 \subset {\rm AdS}_4 \times S^7$ case by a formal analytic continuation.

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arXiv2026

Strong coupling expansion of $1\over 2$ BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS$_5 \times $S$^5$

The exact localization result for the expectation value of the $1\over 2$ BPS circular Wilson loop in ${\cal N}=4$ SYM theory is given in the planar limit by the famous Bessel function expression: $\langle W\rangle = {2N\over \sqrt λ} I_1 ( \sqrt λ)$. Expanded in large $λ$ and expressed in terms of the AdS$_5 \times $S$^5$ string tension $T= {\sqrt λ\over 2π}$ this gives $\langle W\rangle = {\sqrt T\over 2πg_s} e^{2πT} (1- {3\over 16 π} T^{-1} + ...)$.The exponential is matched by the value of the action of the string with the AdS$_2$ world volume while the prefactor comes from the 1-loop GS string correction. Here we address the question of how the subleading $T^{-1}$ term could be reproduced by the 2-loop correction in the corresponding partition function of the AdS$_5 \times $S$^5$ GS string expanded near the AdS$_2$ minimal surface. We find that the string correction contains a non-zero UV logarithmic divergence implying that comparison with the SYM result requires a particular subtraction prescription. We discuss implications of this conclusion for checking the AdS/CFT duality at strong coupling.

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arXiv2026

Energy of toroidal M2 brane in flat 11d background

The supermembrane action is non-linear and a priori non-renormalizable. Still, some quantities in this theory may be free of log UV divergences and thus defined unambiguously. To explore this possibility we compute the energy of an M2 brane wrapped on a 2-torus in flat 11d space to two loops in the inverse-tension expansion. The result is free of logarithmic divergences and the same should hold also at higher loop orders. For fermions periodic around both circles the quantum corrections cancel, consistent with the BPS nature of the wrapped M2 brane state. For fermions antiperiodic around one or both circles the energy is a non-trivial function of the radii given by infinite sums of modified Bessel functions. We also compute 3-loop correction to the energy of the bosonic membrane on $\mathbb R^2\times S^1$. In contrast to the string case, it contains, besides powers of the 1-loop $ζ(3)$ coefficient, a new term proportional to $ζ(9)$. Summing contributions of all-loop bubble graphs leads to a simple cubic equation for the membrane energy. The analogous resummation in the Nambu or GS string t case reproduces the familiar exact square-root expression ${\mathcal E}=\sqrt{(2πR\,T_1)^2+m_0^2}$. We find that the bubble-graph part of the membrane energy does not vanish for any value of the radius $R_{11}$. If contributions of other non-trivial diagrams in the supermembrane case do not qualitatively change this conclusion, this would disfavour the conjectured relation between 11d theory on an antiperiodic circle and the strong-coupling limit of type 0A string theory.

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arXiv2026

2-loop free energy of M2 brane in AdS$_7 \times$ S$^4$ and surface defect anomaly in (2,0) theory

A $\frac{1}{2}$-BPS surface operator viewed as a conformal defect in rank $N$ 6d (2,0) theory is expected to have a holographic description in terms of a probe M2 brane wrapped on AdS$_3$ in the AdS$_7\times S^4$ M-theory background. The M2 brane has an effective tension T$_2= \frac{2}{ π} N$ so that the large tension expansion corresponds to the $1/N$ expansion. The value of the defect conformal anomaly coefficient in $SU(N)$ (2,0) theory was previously argued to be b$=12N- 9 - 3N^{-1}$. At the same time, one may expect that the probe M2 brane ending on a stack of $N$ M5 branes should represent a Wilson surface operator in the $U(N)$ rather than $SU(N)$ boundary 6d CFT. In this case one should get b$=12N- 9 $, i.e. the $N^{-1}$ term (that in the $SU(N)$ expression ensures that b vanishes for $N=1$) should be absent. By semiclassically quantizing M2 brane, it was found in arXiv:2004.04562 that the first two terms in b are indeed reproduced by the classical and 1-loop corrections to the M2 free energy. Here we address the question of the value of the next 2-loop term in the M2 brane free energy, i.e. the coefficient of the $N^{-1}$ term in b. Remarkably, despite the general non-renormalizability of the standard BST M2 brane action we find that the 2-loop correction to the free energy of the AdS$_3$ M2 brane in AdS$_7\times S^4$ is UV finite (modulo power divergences that can be removed by an analytic regularization). Moreover, the 2-loop correction vanishes in both dimensional and $ζ$-function regularizations. This supports the expectation that the M2-brane probe computation captures the surface-defect anomaly of the $U(N)$ rather than the $SU(N)$ boundary 6d theory.

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arXiv2026

Wilson loop in AdS$_3 \times S^3 \times T^4$ from quantum M2 brane

Type IIB string theory on AdS$_3 \times S^3\times T^4$ with RR flux as the near-horizon limit of the D1-D5 solution is expected to be dual to a (4,4) supersymmetric 2d CFT parametrized by the integers $Q_1,Q_5$ and other moduli. It is related by T-duality to type IIA string theory in the near-horizon limit of the D2-D4 solution which admits an uplift to the 11d AdS$_3 \times S^3\times T^5$ background which is the near-horizon limit of the M2-M5 solution. We point out that this relation allows one to use the quantum M2-brane description to probe ``non-planar'' corrections in the dual 2d CFT, in close analogy with the ABJM theory case (described by M-theory on AdS$_4 \times S^7/\mathbb{Z}_k$). We consider an analog of a supersymmetric Wilson loop (line defect) expectation value represented by type IIA string partition function expanded around AdS$_2\subset $AdS$_3$ minimal surface. Its M-theory analog is the M2 brane partition function expanded near AdS$_2\times S^1$. We compute the 1-loop contribution $Z_1$ to the M2 brane partition function and find that in contrast to the ABJM case in arXiv:2303.15207 (where $Z_1= (2\sin{\frac{2π}{ k}})^{-1} = \frac{k}{ 4 π} +\fracπ{ 6k} +...$ contains an infinite series of higher genera string corrections, $k^{-1} \sim \frac{g_s}{ \sqrt {\rm T}}$), here it is given solely by the leading string-theory contribution $Z_1= \fracκ{ \sqrt{2π}}$ where $κ\sim \sqrt{Q_5}$ plays a role analogous to $k$. We also discuss a generalization to the mixed flux case which is straightforward from the 11d perspective.

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arXiv2026

On anomaly free 4d $\mathcal{N}$=4 and 6d (2,0) conformal supergravities and UV finiteness of Poincaré supergravities

We review the structure of superconformal anomalies in 4d $\mathcal N$=4 conformal supergravity (CSG) coupled to a number N$_\rm v$ of $ \mathcal N$=4 vector multiplets and 6d (2,0) CSG coupled to N$_{_{\rm T}}$ of (2,0) tensor multiplets. Anomalies cancel if N$_\rm v$=4 and N$_{_{\rm T}}$=26 respectively. If the CSG part of the action is dropped and N$_{\rm v}$=6+ n$_{\rm v}$, the first theory is classically equivalent to the 4d $\mathcal N$=4 Poincaré supergravity (PSG) coupled to n$_{\rm v}$ vector multiplets, while the second one with N$_{_{\rm T}}$=5+ n$_{_{\rm T}}$ is classically equivalent to the 6d (2,0) PSG coupled to n$_{\rm T}$ tensor multiplets. We argue that these facts imply that divergences in the 4d PSG with n$_{\rm v}$ vectors should be proportional to n$_{\rm v}$+2 and similarly in the 6d PSG with n$_{_{\rm T}}$ tensors to n$_{_{\rm T}}$-21. These predictions appear to be consistent with known results of explicit scattering amplitude computations in these 4d and 6d PSG theories.

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arXiv2026

On world-volume supersymmetry of supermembrane action in static gauge

We review and elaborate on the issue of 3d world volume supersymmetry that appears as a residual part of global target space supersymmetry in the BST supermembrane action. While there is no direct ``spinning membrane'' analog of the world-volume supersymmetric spinning string action that could be obtained by coupling $D$ copies of 3d scalar multiplet to 3d supergravity, we discuss how one may construct an $N=1$ 3d supersymmetric analog of the derivative expansion of the bosonic membrane action in static gauge. We compare the resulting $N=1$ supersymmetric action for eight 3d scalar multiplets to the $N=8$ 3d supersymmetric action describing the $D=11$ supermembrane in the static gauge. The two actions are not equivalent which is related to the fact that the full $N=8$ supersymmetry of the static-gauge $D=11$ supermembrane action can be realised only if the fermions are described by an $SO(8)$ spinor rather than vector. The two actions are still directly related in special dimensions $D=4$ and 5. We also compute the one-loop world-volume scattering amplitudes for the two theories, finding that they indeed agree for $D=4,5$ but disagree for $D=11$.

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arXiv2026

Renormalization Group and String Loops

Fixed points of the 2d renormalization group flow are known to correspond to tree level string vacua. We discuss how the renormalization group (or "sigma model") approach can be extended to the string loop level. The central role of the condition of renormalizability of the generating functional for string amplitudes with respect to both "local" and "modular" infinities is emphasized. Several one-loop and two-loop examples of renormalization are considered. It is found that in order to ensure the renormalizability of the generating functional one is to use an "extended" (Schottky-type) parametrization of the moduli space. An approach to resummation of the string perturbative expansion based on operators of insertion of topological fixtures is suggested.

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arXiv2026

Sigma model approach to string theory

A review of the $σ$-model approach to derivation of effective string equations of motion for the massless fields is presented. We limit our consideration to the case of the tree approximation in the closed bosonic string theory.

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arXiv2025

Strong coupling expansion of circular Wilson loops and string theories in AdS$_5 \times {\rm S}^5$ and AdS$_4 \times {\rm CP}^3$

We revisit the problem of matching the strong coupling expansion of the $\frac{1}{2}$ BPS circular Wilson loops in ${\cal N}=4$ SYM and ABJM gauge theories with their string theory duals in ${\rm AdS}_5 \times S^5$ and ${\rm AdS}_4 \times CP^3$, at the first subleading (one-loop) order of the expansion around the minimal surface. We observe that, including the overall factor $1/g_{\rm s}$ of the inverse string coupling constant, as appropriate for the open string partition function with disk topology, and a universal prefactor proportional to the square root of the string tension $T$, both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the $\sqrt T$ prefactor based on special features of the combination of one-loop determinants appearing in the string partition function. The latter also implies a natural generalization $Z_χ\sim (\sqrt T/g_{\rm s})^χ$ to higher genus contributions with the Euler number $χ$, which is consistent with the structure of the $1/N$ corrections found on the gauge theory side.

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arXiv2025

On world-sheet S-matrix of NSR string in static gauge

As was shown in arXiv:1203.1054, expanding the Nambu action near the "long string" vacuum in the static gauge one finds that the one-loop 2 to 2 scattering amplitude of the $D-2=24$ transverse 2d fluctuations $X^i$ is given by a pure phase expression consistent with underlying integrability. Similar computation in the Green-Schwarz superstring was carried out in arXiv:2404.09658. Here we consider the case of the NSR string starting with its manifestly 2d covariant action given by $D$ scalar multiplets coupled to 2d supergravity. Eliminating the zweibein and gravitino fields is non-trivial, and a Nambu-like formulation of the spinning string involving only scalar coordinates and their 2d fermionic partners has not previously been available. We show how the auxiliary fields can be eliminated in static gauge after a specific choice of superconformal gauge for the fermions, while keeping the transverse fields $X^i$ and $ψ^i$ off-shell. The resulting one-loop S-matrix for $X^i$ is found, as expected, to be the same as in the GS superstring case. We also discuss similar actions for the heterotic string and a $T\bar T$ deformation of free 2d scalar multiplet.

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arXiv2025

On non-planar ABJM anomalous dimensions from M2 branes in AdS$_{4}\times S^{7}/\mathbb{Z}_{k}$

Planar parts of conformal dimensions of primary operators in $U_k(N) \times U_{-k}(N)$ ABJM theory are controlled by integrability. Strong coupling asymptotics of planar dimensions of operators with large spins can be found from the energy of semiclassical strings in AdS$_{4}\times$CP$^3$ but computing non-planar corrections requires understanding higher genus string corrections. As was pointed out in arXiv:2408.10070, there is an alternative way to find the non-planar corrections by quantizing M2 branes in AdS$_{4}\times S^7/\mathbb{Z}_{k}$ which are wrapped around the 11d circle of radius $1/k= λ/N$ and generalize spinning strings in AdS$_4\times$CP$^3$. Computing the 1-loop correction to the energy of M2 brane that corresponds to the long folded string with large spin $S$ in AdS$_4$ allowed to obtain a prediction for the large $λ$ limit of non-planar corrections to the cusp anomalous dimension. Similar predictions were found for non-planar dimensions of operators dual to M2 branes that generalize the ''short'' and ''long'' circular strings with two equal spins $J_1=J_2$ in CP$^3$. Here we consider two more non-trivial examples of 1-loop M2 brane computations that correspond to: (i) long folded string with large spin $S$ in AdS$_4$ and orbital momentum $J$ in CP$^3$ whose energy determines the generalized cusp anomalous dimension, and (ii) circular string with spin $S$ in AdS$_4$ and spin $J$ in CP$^3$. We find the leading terms of the expansion of the corresponding 1-loop M2 brane energies in $1/k$. We also discuss similar semiclassical 1-loop M2 brane computation in flat 11d background and comment on possible relation to higher genus corrections to energies in 10d string theory.

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arXiv2025

Scattering on the supermembrane

We compute the one-loop $2 \rightarrow 2$ scattering amplitude of massless scalars on the world volume of an infinite $D = 11$ supermembrane quantized in the static gauge. The resulting expression is manifestly finite and turns out to be much simpler than in the bosonic membrane case in arXiv:2308.12189 being simply proportional to the tree-level scattering amplitude. We also consider the case of $\mathbb{R}^{1,1} \times S^1$ membrane with one dimension compactified on a circle of radius R and demonstrate how the supermembrane scattering amplitude reduces to the one on an infinite $D = 10$ Green-Schwarz superstring in the limit of R $\rightarrow 0$.

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arXiv2025

S-matrix on effective string and compactified membrane

Expanding Nambu-Goto action near infinitely long string vacuum one can compute scattering amplitudes of 2d massless fields representing transverse string coordinates. As was shown in arXiv:1203.1054, the resulting S-matrix is integrable, in agreement with the known free string spectrum and also with an interpretation of the static-gauge NG action as a $T\bar T$ deformation of a free massless theory. We consider a generalization of this computation to the case of a membrane, expanding its 3d action near an infinite membrane vacuum that has cylindrical $\mathbb R \times S^1$ shape (we refer to such membrane as "compactified"). Representing 3d fields as Fourier series in $S^1$ coordinate we get an effective 2d model in which the massless string modes are coupled to an infinite KK tower of massive 2d modes. We find that the resulting 2d S-matrix is not integrable already at the tree level. We also compute 1-loop scattering amplitude of massless string modes with all compactified membrane modes propagating in the loop. The result is UV finite and is a non-trivial function of the kinematic variables. In the large momentum limit or when the radius of $S^1$ is taken to infinity we recover the expression for the 1-loop scattering amplitude of the uncompactified $\mathbb R^2$ membrane. We also consider a 2d model which is the $T\bar T$ deformation to the free theory with the same massless plus infinite massive tower of modes. The corresponding 2d S-matrix is found, as expected, to be integrable.

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arXiv2025

Non-planar corrections to ABJM Bremsstrahlung function from quantum M2 brane

As was shown in arXiv:2303.15207, the leading large $N$, fixed $k$ correction in the localization result for the expectation value of the $\frac{1}{2}$-BPS circular Wilson loop in $U(N)_{k}\times U(N)_{-k}$ ABJM theory given by the $(\sin\frac{2π}{ k})^{-1}$ factor can be reproduced on the dual M-theory side as the one-loop correction in the partition function of an M2 brane in AdS$_{4}\times S^{7}/\mathbb{Z}_{k}$ with AdS$_{2}\times S^{1}$ world volume. Here we prove, following the suggestion in arXiv:2408.10070, that the analogous fact is true also for the corresponding correction $B_1=-\frac{1}{2πk}\cot\frac{2π}{k}$ in the localization result for the Bremsstrahlung function associated with the Wilson line with a small cusp in either AdS$_4$ or $\rm CP^3$. The corresponding M2 brane is wrapped on the 11d circle and generalizes the type IIA string solution in AdS$_{4}\times \rm CP^3$ ending on the cusped line. We show that the one-loop term in the M2 brane partition function reproduces the localization expression for $B_1$ as the coefficient of the leading term in its small cusp expansion.

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arXiv2025

Semiclassical quantization of M5 brane probes wrapped on $\textrm{AdS}_3\times S^3$ and defect anomalies

We consider two supersymmetric M5 brane probe solutions in $\textrm{AdS}_7 \times S^4$ and one in $\textrm{AdS}_4 \times S^7$ that all have the $\textrm{AdS}_3 \times S^3$ world-volume geometry. The values of the classical action of the first two M5 probes (with $S^3$ in $\textrm{AdS}_7$ or in $S^4$) are related to the leading $N^2$ parts in the anomaly b-coefficient in the (2,0) theory corresponding to a spherical surface defect in symmetric or antisymmetric $SU(N)$ representations. We present a detailed computation of the corresponding one-loop M5 brane partition functions finding that they vanish (in a particular regularization). This implies the vanishing of the order $N^0$ part in the b-anomaly coefficients, in agreement with earlier predictions for their exact values. It remains, however, a puzzle of how to reproduce the non-vanishing order $N$ terms in these coefficients within the semiclassical M5-brane probe setup.

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arXiv2024

Non-planar corrections in ABJM theory from quantum M2 branes

The quantization of semiclassical strings in AdS spacetimes yields predictions for the strong-coupling behaviour of the scaling dimensions of the corresponding operators in the planar limit of the dual gauge theory. Finding non-planar corrections requires computing string loops (corresponding to torus and higher genus surfaces), which is a challenging task. It turns out that in the case of the $U_k(N) \times U_{-k}(N)$ ABJM theory there is an alternative approach: one may semiclassically quantize M2 branes in AdS$_{4}\times S^7/\mathbb{Z}_{k}$ which are wrapped around the 11d circle of radius $1/k= λ/N$. Such M2 branes are the M-theory generalization of the strings in AdS$_4\times $CP$^3$. In this work, we show that by expanding in large M2 brane tension $ T_2 \sim \sqrt{kN} $ for fixed $k$, followed by an expansion in large $k$, we can predict the large $λ$ asymptotics of the non-planar corrections to the dimensions of the dual ABJM operators. As a specific example, we consider the M2 brane configuration that generalizes the long folded string with large spin in AdS$_4$, and compute the 1-loop correction to its energy. This calculation allows us to determine non-planar corrections to the universal scaling function or cusp anomalous dimension. We extend our analysis to the semiclassical M2 branes that generalize the "short" and "long" circular strings with two equal angular momenta in CP$^3$. The "short" M2 brane corresponds to a dual operator whose dimension at strong coupling scales as $Δ\sim λ^{1/4} + \dots$, and we derive the leading non-planar correction to it.

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arXiv2024

On co-dimension 2 defect anomalies in N=4 SYM and (2,0) theory via brane probes in AdS/CFT

We consider a $\frac{1}{2}$-BPS solution for a D3 brane probe in AdS$_5 \times S^5$ that has world-volume geometry of AdS$_3 \times S^1$. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary N=4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS$_3$ and may thus be interpreted as computing conformal anomaly of the supersymmetric $S^2$ defect. The classical action scales as $N$. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a $\frac{1}{2}$-BPS M5 brane probe solution in AdS$_7 \times S^4$ with the world-volume geometry of AdS$_5 \times S^1$ that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order $N^2$ term in $a$-anomaly of the supersymmetric $S^4$ defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the $S^4$ defect $a$-anomaly coefficient.

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