T-duality without isometry via extended gauge symmetries of 2D sigma models

Abstract

Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.

Hidden isometry of “T-duality without isometry”

“…We do not give the complete account of all possible cases (the interested reader can find it in [1,2,5,8]), because our concern is different. We will show that the Lie algebroid generalisation of the intermediate gauge theory proposed by CDJ in [3] can be rewritten, using appropriate field redefinitions, in the standard non-Abelian T-duality form (2.4). It follows that the CDJ proposal cannot describe more general T-duality patterns than that of traditional non-Abelian T-duality.…”

“…In Section 6, we illustrate a few examples where, by simple field redefinitions, the traditional isometric Roček-Verlinde gauge theory may look like a non-trivial Lie algebroid gauge theory. In particular, we unmask the "non-isometric T-duality" example of CDJ presented in [3]. Finally, we end with a short discussion.…”

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We study the T-dualisability criteria of Chatzistavrakidis, Deser and Jonke [3] who recently used Lie algebroid gauge theories to obtain sigma models exhibiting a "T-duality without isometry". We point out that those T-dualisability criteria are not written invariantly in [3] and depend on the choice of the algebroid framing. We then show that there always exists an isometric framing for which the Lie algebroid gauging boils down to standard Yang-Mills gauging.

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Momentum Sections in Hamiltonian Mechanics and Sigma Models

“…Recently, a two-dimensional gauged sigma model with a two-form b-field with three dimensional Wess-Zumino term [14] is analyzed related to T-duality in string theory [4,5,7,8,9,10]. For such an application, it is interesting to generalize a momentum section in a pre-multisymplectic manifold.…”

Lie algebroid gauging of non-linear sigma models

“…However, there are subtleties to consider when attempting to apply this to the study of non-linear sigma models. When this procedure was applied to the study of T-duality there was an initial belief that it let to a notion of 'non-isometric T-duality' [4,6]. It was later shown that gauge invariance of the action actually rendered the non-isometric T-duality proposal equivalent to non-abelian T-duality [2].…”