On quantum T-duality in sigma models

Nuclear Physics B - Proceedings Supplements, 1996

Various examples of target space duality transformations are investigated up to two loop order in perturbation theory. Our results show that when using the tree level ('naive') transformation rules the dual theories are in general inequivalent at two loops to the original ones, (both for the Abelian and the non Abelian duality).

Physical Review D

Exact conformal field theories (CFTs) are obtained by using the approach of Poisson-Lie (PL) T-duality in the presence of spectators. We explicitly construct some non-Abelian T-dual σ-models (here as the PL T-duality on a semi-Abelian double) on 2 + 2-dimensional target manifolds M ≈ O×G andM ≈ O×G, where G andG as two-dimensional real non-Abelian and Abelian Lie groups act freely on M andM , respectively, while O is the orbit of G in M. The findings of our study show that the original models are equivalent to Wess-Zumino-Witten (WZW) models based on the Heisenberg (H4) and GL(2, R) Lie groups. In this way, some new T-dual backgrounds for these WZW models are obtained. For one of the duals of the H4 WZW model, we show that the model is self-dual. In the case of the GL(2, R) WZW model it is observed that the duality transformation changes the asymptotic behavior of solutions from AdS3 × R to flat space. Then, the structure and asymptotic nature of the dual spacetime of this model including the horizon and singularity are determined. We furthermore get the non-critical Bianchi type III string cosmological model with a non-vanishing field strength from T-dualizable σ-models and show that this model describes an exact CFT (equivalent to the GL(2, R) WZW model). After that, the conformal invariance of T-dual models up to two-loop order (first order in α ′) is discussed.

Physics Letters B, 1997

It is a well known fact that the classical ("Buscher") transformations of T-duality do receive, in general, quantum corrections. It is interesting to check whether classical T-duality can be exact as a quantum symmetry. The natural starting point is a σ-model with N=4 world sheet supersymmetry. Remarkably, we find that (owing to the fact that N=4 models with torsion are not off-shell finite as quantum theories),the T-duality transformations for these models get in general quantum corrections, with the only known exception of warped products of flat submanifolds or orbifolds thereof with other geometries.

Nuclear Physics B, 1996

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear σ-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the boson-fermion symphysis of the dual transition, and on the new geometry of the DSM. 1 i.e. preserve canonical commutation relations. Canonical transformations in quantum mechanics underlie Dirac's path integral formulation [4], and have been discussed extensively in field theory, e.g. [5, 6, 7].

Journal of High Energy Physics, 2004

We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy the vanishing β-function equations with constant dilaton field. Using the Poisson-Lie T-plurality we then construct 3-dimensional sigma models that correspond to various decompositions of Drinfeld double. Models with nontrivial dilaton field may appear. It turns out that for "traceless" dual algebras they satisfy the vanishing β-function equations as well. In certain cases the dilaton cannot be defined in some of the dual models. We provide an explanation why this happens and give criteria predicting when it happens.

Journal of High Energy Physics, 2014

A recent claim that the S-duality between 4d SUSY gauge theories, which is AGT related to the modular transformations of 2d conformal blocks, is no more than an ordinary Fourier transform at the perturbative level, is further traced down to the commutation relation [P ,Q] = −i between the check-operator monodromies of the exponential resolvent operator in the underlying Dotsenko-Fateev matrix models and βensembles. To this end, we treat the conformal blocks as eigenfunctions of the monodromy check operators, what is especially simple in the case of one-point toric block. The kernel of the modular transformation is then defined as the intertwiner of the two monodromies, and can be obtained straightforwardly, even when the eigenfunction interpretation of the blocks themselves is technically tedious. In this way, we provide an elementary derivation of the old expression for the modular kernel for the one-point toric conformal block.

Physical Review D, 1995

A generating functional $F$ is found for a canonical nonabelian dual transformation which maps the supersymmetric chiral O(4) $\sigma$-model to an equivalent supersymmetric extension of the dual $\sigma$-model. This $F$ produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a {\em symphysis} of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional $T$ which relates wavefunctions in the two quantum theories is argued to be {\em exactly} given by $T=\exp(iF)$.

1998

Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the dual pair of σ-models defined by the double SO(3,1) in the Iwasawa decomposition.

Physical Review D, 2000

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU (2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.

J High Energy Phys, 2010

In this note we consider a fermionic T-duality of the coset realization of the type IIA sigma-model on AdS 4 × CP 3 with respect to the three flat directions in AdS 4 , six of the fermionic coordinates and three of the CP 3 directions. We show that the Buscher procedure fails as it leads to a singular transformation and discuss the result and its implications.