On integrable backgrounds self-dual under fermionic T-duality

Physics Letters B, 2013

We study the action of non-Abelian T-duality in the context of N = 1 geometries with well understood field theory duals. In the conformal case this gives rise to a new solution that contains an AdS 5 × S 2 piece. In the case of non-conformal geometries we obtain a new background in massive IIA supergravity that presents similar behaviour to the cascade of Seiberg dualities. Some physical observables are discussed. * gitsios@upatras.gr

Journal of Physics A: Mathematical and General, 2004

Journal of High Energy Physics, 2015

We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no AdS n backgrounds with n ≠ 3. Moreover the warp factor of AdS3 backgrounds is constant, the geometry is a product AdS 3 × M 7 and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of M 7 has been specified in all cases. For 2 supersymmetries, it has been found that M 7 admits a suitably restricted G 2 structure. For 4 supersymmetries, M 7 has an SU(3) structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, M 7 has an SU(2) structure and can be described locally as a S 3 fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-Kähler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of α′ corrections.

Nuclear Physics B, 1998

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl anomaly coefficients of the original and dual theories. The analysis is not restricted to conformally invariant backgrounds. The formalism is applied to the study of two examples. The first is a model based on SU(2) non-Abelian T duality. The second represents a simple realization of Poisson-Lie T duality involving the Drinfeld double based on SU(2). In both cases quantum T duality is established at the 1-loop level.

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].

Physics Letters B, 2007

We consider two dimensional non linear sigma models on few symmetric superspaces, which are supergroup manifolds of coset type. For those spaces where one loop beta function vanishes, two loop beta function is calculated and is shown to be zero. Vanishing of beta function in all orders of perturbation theory is shown for the principal chiral models on group supermanifolds with zero Killing form. Sigma models on symmetric (super) spaces on supergroup manifold G/H are known to be classically integrable. We investigate a possibility to extend an argument of absence of quantum anomalies in non local current conservation from non super case to the case of supergroup manifolds which are asymptotically free in one loop.

Journal of High Energy Physics, 2012

In this paper we continue the study, initiated in [1, 2], of the classical integrability of Green-Schwarz superstrings in AdS 4 × CP 3 and AdS 2 × S 2 × T 6 superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z 4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z 4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS 4 × CP 3 and AdS 2 × S 2 × T 6 superstring sigma-models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32 = 24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS 2 × S 2 × T 6 superspace to all orders in the coset fermions and to the second order in the non-coset ones. B Superstring equations of motion on AdS 4 × CP 3 to the second order in υ 20 C Curvature of the Lax connection 21 D Gamma-matrix identities 23 D.

1996

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear sigma-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.

Nuclear Physics B, 1998

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl anomaly coefficients of the original and dual theories. The analysis is not restricted to conformally invariant backgrounds. The formalism is applied to the study of two examples. The first is a model based on SU (2) non-Abelian T duality. The second represents a simple realization of Poisson-Lie T duality involving the Drinfeld double based on SU (2). In both cases quantum T duality is established at the 1-loop level.

arXiv: High Energy Physics - Theory, 2017

AdS/CFT is a conjectured equivalence between a field theory without gravity (conformal field theory) and a string theory in a special curved background (anti de-Sitter space), where theories on both sides of the equivalence is supersymmetric. Since the nature as we observe at low energy is non-supersymmetric, it will be very useful if we can have this conjecture in the non-supersymmetric case. Here we will give some evidence that AdS/CFT type duality must work for non-supersymmetric system. We will indicate some calculation which leads us to such conclusion.