arXiv subjects

Matthias R. Gaberdiel

Publications and source records attributed to Matthias R. Gaberdiel.

At least 19 recordsLinked to original sources

arXiv2026

$\mathcal{N}=2$ RG flows, Non-Invertible Symmetries and Matrix Factorisations

We study the behaviour of the topological defect lines of the $k^{\rm th}$ ${\cal N}=2$ minimal models that are preserved by the least relevant perturbation to first order. It is usually believed that these defects should then also define symmetries of the IR theory, which for the usual "massless'' flow should be the $(k-2)^{\rm nd}$ ${\cal N}=2$ minimal model. Using CFT arguments we show that this is not possible. We also reproduce this result using matrix factorisation techniques: while the corresponding B-type defects can be adjusted to first order in the deformation, there is an obstruction at second order, which is associated with a supersymmetry anomaly. By contrast, for the associated massive integrable flow, which corresponds to a Chebyshev deformation of the superpotential, all of these defects can be consistently deformed, and they indeed define symmetries of the massive IR theory.

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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.

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arXiv2026

Defects in N=1 minimal models and RG flows

Utilising the symmetry constraints of suitable topological defects, the possible RG flows of N=1 superconformal minimal models are studied. We first employ a coset description that only captures the bosonic subalgebra, and then generalise the discussion to the actual superconformal models.

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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 $w$.

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arXiv2026

A localising AdS$_3$ sigma model

We construct a CFT with $\mathfrak{sl}(2,\mathbb{R})_k$ symmetry at the `tensionless' point $k=3$, which is distinct from the usual $\mathrm{SL}(2,\mathbb{R})_{k=3}$ WZW model. This new CFT is much simpler than the generic WZW model: in particular its three-point functions feature momentum-conserving delta functions, and its higher-point functions localise to covering map configurations in moduli space. We establish the consistency of the theory by explicitly deriving the four-point function from the three-point data via a sum over conformal blocks. The main motivation for our construction comes from holography, and we show that various simple supersymmetric holographic dualities for $k_{\rm s}=1$ ($k=3$) can be constructed by replacing the $\mathrm{AdS}_3$ factor on the worldsheet with this alternative theory. This includes in particular the prototypical case of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$, as well as the recently discussed example of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$. However, our analysis does not require supersymmetry and also applies to bosonic ${\rm AdS}_3$ backgrounds (at $k=3$).

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arXiv2025

Structure of the $\mathcal{N}=4$ chiral algebra

The chiral algebra of 4D $\mathcal{N}=4$ SU$(N)$ super-Yang-Mills theory is an $\mathcal{N}=4$ superconformal vertex operator algebra. We analyse the structure of this algebra by studying recursively the constraints that are required by the associativity of the operator product expansion. We find that the algebra is uniquely characterized by the central charge (which can take an arbitrary value), without any additional free parameter. Furthermore, the truncation pattern of the OPE coefficients suggests that the algebra cannot arise from the symmetric orbifold.

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arXiv2025

Correlators for tensionless strings on ${\rm AdS}_3$ orbifolds

The CFT dual of string theory on $({\rm AdS}_3 \times {\rm S}^3)/\mathbb{Z}_k\times \mathbb{T}^4$ is believed to be described by the subspace of the symmetric orbifold of $\mathbb{T}^4$ that comprises the low-lying excitations on top of a certain reference state. (This `non-perturbative' reference state lies in the twisted sector associated to the conjugacy class consisting of only $k$-cycles.) In a recent paper we confirmed this picture by analysing the worldsheet theory of the orbifold at the tensionless NS-NS point, and by showing that the perturbative worldsheet spectrum reproduces precisely the single particle excitations on top of this reference state. In this paper we explain that this identification also holds on the level of the correlators, at least to leading order in $1/N$.

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arXiv2025

The Triplet Perturbation of the Symmetric Orbifold

The perturbation of the symmetric orbifold of $\mathbb{T}^4$ under the triplet of exactly marginal operators from the $2$-cycle twisted sector is studied in perturbation theory. We show that the structure of the triplet perturbation is very similar to that of the previously studied singlet perturbation, and in particular, that the theory remains also integrable in this case. Furthermore, using the various symmetries of the problem, we identify the dual supergravity interpretation of these deformations.

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arXiv2025

D-Branes in $\textbf{AdS}_3\times \textbf{S}^3 \times \textbf{S}^3 \times \textbf{S}^1$

String theory on $\mathrm{ AdS}_3\times \mathrm{ S}^3 \times \mathrm{ S}^3 \times \mathrm{S}^1$ with two units of NS flux through each of the two $3$-spheres (and one unit of NS flux supporting the $\mathrm{AdS}_3$ factor) was recently argued to be exactly dual to the symmetric orbifold of eight free fermions and two bosons. This setup is interesting since it allows for a simple NS-R description. In this paper we study the spherical D-branes of this theory, and identify them with branes in the dual symmetric orbifold theory. We also comment briefly on the $\mathrm{ AdS}_2$ branes.

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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.

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arXiv2024

Tensionless strings on $AdS_3 \times S^3 \times S^3 \times S^1$

We propose that string theory on ${\rm AdS}_3 \times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1$ with $\textit{two}$ units of NS-NS flux through each of the two $3$-spheres is exactly dual to the symmetric orbifold of $2$ bosons and $8$ free fermions. Here, one of the two bosons describes the compact ${\rm S}^1$, while the other one corresponds to the radial (non-compact) direction of ${\rm AdS}_3$. Unlike the analogous situation for ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$, the description makes sense both in the NS-R as well as the hybrid formulation, and we explain the duality in both frameworks.

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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.

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arXiv2023

The $\mathfrak{u}(2|2)_1$ WZW model

WZW models based on super Lie algebras play an important role for the description of string theory on AdS spaces. In particular, for the case of ${\rm AdS}_3 \times {\rm S}^3$ with pure NS-NS flux the super Lie algebra of $\mathfrak{psu}(1,1|2)_k$ appears in the hybrid formalism, and higher dimensional AdS spaces can be described in terms of related supergroup cosets. In this paper we study the WZW models based on $\mathfrak{u}(2|2)_1$ and $\mathfrak{psu}(2|2)_1$ that may play a role for the worldsheet theory that is dual to free super Yang-Mills in 4D.

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arXiv2023

Tensionless strings on ${\rm AdS}_3$ orbifolds

The bound state of one NS5 brane (wrapped on a $\mathbb{T}^4$) and $N$ NS1-branes has two dual descriptions: its low-energy dynamics is described by the symmetric orbifold of $\mathbb{T}^4$, while the near horizon geometry is captured by string theory on ${\rm AdS}_3 \times {\rm S}^3\times \mathbb{T}^4$ with one unit of NS flux. The latter theory is exactly solvable in the hybrid formalism, and this allows one to prove the equivalence of the two descriptions. In this paper we extend this duality to $\mathbb{Z}_k$ orbifolds of this ${\rm AdS}_3 \times {\rm S}^3$ background. In particular, we show that the corresponding worldsheet spectrum reproduces exactly the perturbative excitations on top of a certain non-perturbative state in the dual symmetric orbifold theory. Since the ${\rm AdS}/{\rm CFT}$ duality map is exact for these models, we obtain an interesting picture of how the duality relates boundary and bulk descriptions.

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arXiv2022

Perturbing the symmetric orbifold from the worldsheet

The symmetric orbifold of $\mathbb{T}^4$ is the analogue of free SYM in four dimensions, and its dual is described by a tensionless string propagating in ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$. In this paper we study the deformation of this exact AdS/CFT duality away from the free point. On the symmetric orbifold side this amounts to perturbing the theory by the exactly marginal operator from the $2$-cycle twisted sector. We identify the corresponding perturbation in the dual worldsheet description, and show that the anomalous conformal dimensions of a number of symmetric orbifold currents are correctly reproduced from this worldsheet perspective.

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arXiv2022

Worldsheet dual of free $\mathcal{N}=2$ quiver gauge theories

For a special family of 4d $\mathcal{N}=2$ superconformal quiver theories, the worldsheet dual corresponding to the free theory is identified. This result is obtained from the recently proposed worldsheet dual of free $\mathcal{N}=4$ SYM by applying a $\mathbb{Z}_k$ orbifold. In support of our proposal we show that the spectrum of both the untwisted as well as the twisted sectors coincides between the two descriptions.

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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.

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arXiv2022

The free field realisation of the BVW string

The symmetric orbifold of $\mathbb{T}^4$ was recently shown to be exactly dual to string theory on ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal ($k=1$) NS-NS flux. The worldsheet theory is best formulated in terms of the hybrid formalism of Berkovits, Vafa & Witten (BVW), in terms of which the ${\rm AdS}_3\times {\rm S}^3$ factor is described by a $\mathfrak{psu}(1,1|2)_k$ WZW model. At level $k=1$, $\mathfrak{psu}(1,1|2)_1$ has a free field realisation that is obtained from that of $\mathfrak{u}(1,1|2)_1$ upon setting a $\mathfrak{u}(1)$ field, often called $Z$, to zero. We show that the free field version of the ${\cal N}=2$ generators of BVW (whose cohomology defines the physical states) does not give rise to an ${\cal N}=2$ algebra, but is rather contaminated by terms proportional to the $Z$-field. We also show how to overcome this problem by introducing additional ghost fields that implement the quotienting by $Z$.

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