arXiv subjects

Stefan A. Kurlyand

Publications and source records attributed to Stefan A. Kurlyand.

6 recordsLinked to original sources

arXiv2026

Monopoles on the edge

Quantum M2-brane instantons are studied in eleven-dimensional Freund-Rubin backgrounds. The construction uses the identification of the Calabi-Yau cone over the Sasaki-Einstein manifold $\mathrm{SE}_7$ with the geometric branch of the abelian moduli space of the dual superconformal field theory. A class of BPS cycles in $\mathrm{SE}_7$ wrapped by M2-branes is identified as links of two-dimensional holomorphic cones whose coordinate rings contain BPS monopole operators. The algebraic structure and R-charge assignment on the moduli space further allow the computation of both the classical exponents and one-loop partition functions of the corresponding M2-brane instantons. Several three-dimensional superconformal field theories are analysed explicitly, and the relation to the corresponding localisation matrix models is discussed.

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arXiv2026

Membrane instantons and non-perturbative effects in $\mathrm{AdS}_{4}/\mathrm{CFT}_{3}$

We study Euclidean M2-brane instantons in Freund-Rubin backgrounds $\mathrm{AdS}_{4}\times \mathrm{Y}_7$. For a seven-dimensional weak $G_{2}$ manifold $\mathrm{Y}_7$, we show that the BPS condition for an M2-brane wrapping a three-cycle $Σ\subset \mathrm{Y}_7$ is equivalent to the associativity condition with respect to the nearly parallel $G_{2}$-structure. When $\mathrm{Y}_7$ is Sasaki-Einstein, we identify a special class of BPS M2-branes that preserve both real internal Killing spinors and correspond to invariant three-dimensional submanifolds inheriting a Sasakian structure. We analyse the quadratic fluctuations around BPS M2-brane instantons in these backgrounds. For the special class of M2-branes in Sasaki-Einstein manifolds, the fluctuation problem reduces to transversely elliptic complexes, and the one-loop partition function can be expressed in terms of the corresponding equivariant indices. We then apply the index formula for the one-loop partition function to invariant M2-branes in $S^{7}/\mathbb{Z}_{k}$, recovering the known result for the $S^3/\mathbb{Z}_k$ instantons and discussing more general invariant BPS cycles. As a further application, we consider M2-brane instantons with $S^3$-quotient worldvolumes in the $(p,q)$-model geometry.

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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

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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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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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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