arXiv subjects

Vladimir Mitev

Publications and source records attributed to Vladimir Mitev.

25 records · Page 2Linked to original sources

arXiv2013

Spectra of Coset Sigma Models

We compute the complete 1-loop spectrum of anomalous dimensions for the bulk fields of non-linear sigma models on symmetric coset (super)spaces G/H, both with and without world-sheet supersymmetry. In addition, we provide two new methods for the construction of partition functions in the infinite radius limit and demonstrate their efficiency in the case of (super)sphere sigma models. Our results apply to a large number of target spaces including superspheres and superprojective spaces such as the N=2 sigma model on CP(3|4).

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arXiv2012

Anomalous Dimensions in Deformed WZW Models on Supergroups

We investigate a class of current-current, Gross-Neveu like, perturbations of WZW models in which the full left-right affine symmetry is broken to the diagonal global algebra only. Our analysis focuses on those supergroups for which such a perturbation preserves conformal invariance. A detailed calculation of the 2-point functions of affine primary operators to 3-loops is presented. Furthermore, we derive an exact formula for the anomalous dimensions of a large subset of fields to all orders in perturbation theory. Possible applications of our results, including the study of non-perturbative dualities, are outlined.

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arXiv2012

Conformal superspace sigma-models

We review recent developments in the context of two-dimensional conformally invariant sigma-models. These quantum field theories play a prominent role in the covariant superstring quantization in flux backgrounds and in the analysis of disordered systems. We present supergroup WZW models as primary examples of logarithmic conformal field theories, whose structure is almost entirely determined by the underlying supergeometry. In particular, we discuss the harmonic analysis on supergroups and supercosets and point out the subtleties of Lie superalgebra representation theory that are responsible for the emergence of logarithmic representations. Furthermore, special types of marginal deformations of supergroup WZW models are studied which only exist if the Killing form is vanishing. We show how exact expressions for anomalous dimensions of boundary fields can be derived using quasi-abelian perturbation theory. Finally, the knowledge of the exact spectrum is used to motivate a duality between the OSP(4|2) symmetric Gross-Neveu model and the S(3|2) supersphere sigma-model.

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arXiv2010

Cohomological Reduction of Sigma Models

This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target space supersymmetry algebra can be used to identify subsectors which are often simpler than the original model and may allow for an explicit computation of correlation functions. After an extensive discussion of the general reduction scheme, we present a number of interesting examples, including symmetric superspaces $G/G^{\mathbb{Z}_2}$ and coset superspaces of the form $G/G^{\mathbb{Z}_4}$.

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arXiv2009

The Sigma Model on Complex Projective Superspaces

The sigma model on complex projective superspaces CP^{S-1|S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle θ. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we propose a spin chain regularization of the CP^{S-1|S} model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis.

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arXiv2008

Principal Chiral Model on Superspheres

We investigate the spectrum of the principal chiral model (PCM) on odd-dimensional superspheres as a function of the curvature radius R. For volume-filling branes on S^{3|2}, we compute the exact boundary spectrum as a function of R. The extension to higher dimensional superspheres is discussed, but not carried out in detail. Our results provide very convincing evidence in favor of the strong-weak coupling duality between supersphere PCMs and OSP(2S+2|2S) Gross-Neveu models that was recently conjectured by Candu and Saleur in arXiv:0801.0444.

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arXiv2007

Permutation Orientifolds

We consider orientifold actions involving the permutation of two identical factor theories. The corresponding crosscap states are constructed in rational conformal field theory. We study group manifolds, in particular the examples $SU(2) \times SU(2)$ and $U(1)\times U(1)$ in detail, comparing conformal field theory results with geometry. We then consider orientifolds of tensor products of N=2 minimal models, which have a description as coset theories in rational conformal field theory and as Landau Ginzburg models. In the Landau Ginzburg language, B-orientifolds and D-branes are described in terms of matrix factorizations of the superpotential. We match the factorizations with the corresponding crosscap states.

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