arXiv subjects

Beat Nairz

Publications and source records attributed to Beat Nairz.

6 recordsLinked to original sources

arXiv2026

Non-planar corrections in the symmetric orbifold

We calculate the non-planar corrections to the anomalous dimensions of certain quarter BPS states in the symmetric product orbifold $\text{Sym}^N \big({\mathbb{T}^4}\big)$. We find that some of the degeneracies in the spectrum for large twist $w$ and large $N$ are lifted by these contributions. We furthermore find signatures of quantum chaos, namely level repulsion and random matrix statistics. This suggests that integrability is only present in the symmetric orbifold in the planar (i.e. large $N$) limit.

hep-th↗

arXiv2026

Anomalous dimensions in the symmetric orbifold

Recently, the anomalous conformal dimensions of the symmetric orbifold under the $2$-cycle twisted sector deformation were calculated using the perturbed action of the supercharges. In particular, explicit and simple formulae for the dispersion relations of the torus magnons in the $w$-cycle twisted sector were derived for large $w$. In this paper we reproduce these results from a direct perturbed $2$-point function calculation. In the process we also develop techniques (and a Mathematica code) that allows one to do these calculations for arbitrary quarter BPS states at finite $w$.

hep-th↗

arXiv2026

Super Covering Maps

We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of superconformal field theories, as well as in the hybrid formalism for tensionless string theory on $\text{AdS}_3\times S^3\times\mathbb{T}^4$. In the former, they can be used to calculate correlators in a manifestly supersymmetric way, while in the latter they solve Ward identities of correlators with spacetime supersymmetry.

hep-th↗

arXiv2024

AdS$_3\times$S$^3$ magnons in the symmetric orbifold

The AdS$_3\times$S$^3$ excitations of string theory on AdS$_3\times$S$^3\times \mathbb{T}^4$ are identified with certain collective modes in the dual symmetric orbifold. Our identification follows from a careful study of the conformal eigenstates in the perturbed orbifold theory. We find that, in addition to the fractional torus modes (that correspond to the torus excitations in the dual AdS spacetime), there are `long' collective eigenmodes that involve a superposition of products of fractional torus modes, and that are in natural one-to-one correspondence with the expected AdS$_3\times$S$^3$ excitations. These collective modes are deformations of (fractional) $\mathcal{N}=4$ modes, to which they reduce for integer momentum.

hep-th↗

arXiv2024

Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold

The symmetric orbifold of $\mathbb{T}^4$ is exactly dual to string theory on $\mathrm{AdS}_3\times \mathrm{S}^3 \times \mathbb{T}^4$ with minimal ($k=1$) NS-NS flux. In this paper we study the perturbation of the symmetric orbifold that is dual to switching on R-R flux, and hence to deforming the theory away from the tensionless point. More specifically, we determine systematically the action of a centrally extended supersymmetry algebra on the CFT states, and deduce from it the anomalous conformal dimensions. In the $w$-twisted sector with large $w$ the structure is similar to what was found for $\mathcal{N}=4$ SYM: the basic excitations are multi-magnons whose individual dispersion relation is fixed by symmetry, and the comparison with the BMN answer suggests that the result is true to all orders in perturbation theory. Finally we show that the multi-magnon states interact via an integrable $S$-matrix and possess a natural family of bound states.

hep-th↗

arXiv2022

BPS Correlators for $\text{AdS}_3/\text{CFT}_2$

The BPS correlators of the symmetric product orbifold $\text{Sym}_N(\mathbb{T}^4)$ are reproduced from the dual worldsheet theory describing strings on $\text{AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with minimal ($k=1$) NS-NS flux. More specifically, we show that the worldsheet duals of the symmetric orbifold BPS states can be identified with their lift to the covering surface, thereby making the matching of the correlators essentially manifest. We also argue that the argument can be generalised to arbitrary descendants, using suitable DDF operators on the worldsheet.

hep-th↗