T-dual Backgrounds Research Articles

Holographic duals of N=1 quivers in 5d and their nonrelativistic limits

We explore nonrelativistic limits of $\mathcal{N}=1$ quiver gauge theories in 5d. The stringy counterpart of these Super Conformal Field Theories (SCFTs) is characterized by torsional string Newton-Cartan (TSNC) sigma models which are defined over non-Lorentzian manifolds. We further show that under transverse T duality, these TSNC sigma models are mapped into another new class of nonrelativistic sigma models which are defined over a T-dual TSNC background. Considering nonrelativistic limits of various field theory observables in a holographic setup, we further estimate corresponding entities in the TSNC limit of $\mathcal{N}=1$ quivers. We carry out a parallel analysis on holomorphic functions and the associated pole structures in the nonrelativistic limit of ($p$, $q$) five brane webs. In particular, we investigate the generic structure of various loop operators in a nonrelativistic setup and explore their properties under S duality. Finally, we comment on the large $c$ limit of Ramond-Ramond (RR) fields and discuss the associated S-duality transformation rules in the nonrelativistic limit of $\mathcal{N}=1$ quivers.

New AdS2 supergravity duals of 4d SCFTs with defects

We construct new families of AdS2× S2× S2 solutions with 4 supercharges in Type II supergravities. We show that subclasses of these solutions can be interpreted in terms of defect branes embedded in 4d mathcal{N} = 4 SYM, or orbifolds thereof. This is explicitly realised by showing that the solutions asymptote locally to AdS5× S5/ℤn, in Type IIB, or its T-dual background, in Type IIA. The latter is a Gaiotto-Maldacena geometry realised on an intersection of D4 and NS5 branes. We extend the Type IIA solutions to include D6 branes, and interpret them as describing backreacted baryon vertices within 4d mathcal{N} = 2 CFTs living in D4-NS5-D6 intersections. We propose explicit quiver quantum mechanics in which the defect branes play the role of colour branes, with the D4 branes of the D4-NS5-D6 intersection becoming flavour branes. These quivers are used to compute the degeneracies of the ground states of the dual super conformal quantum mechanics, that are shown to agree with the holographic expressions.

Note about canonical description of T-duality along light-like isometry

In this short note we analyze canonical description of T-duality along light-like isometry. We show that T-duality of relativistic string theory on this background leads to non-relativistic string theory action on T-dual background.

Exact conformal field theories from mutually T-dualizable σ -models

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 $\sigma$-models (here as the PL T-duality on a semi-Abelian double) on $2+2$-dimensional target manifolds $M \approx O \times \bf G$ and ${\tilde M} \approx O \times {\bf {\tilde G}}$, where $\bf G$ and ${\bf {\tilde G}}$ as two-dimensional real non-Abelian and Abelian Lie groups act freely on $M$ and $\tilde M$, respectively, while $O$ is the orbit of $\bf G$ in $M$. The findings of our study show that the original models are equivalent to Wess-Zumino-Witten (WZW) models based on the Heisenberg $(H_4)$ and $GL(2,\mathbb{R})$ Lie groups. In this way, some new T-dual backgrounds for these WZW models are obtained. For one of the duals of the $H_4$ WZW model, we show that the model is self-dual. In the case of the $GL(2,\mathbb{R})$ WZW model it is observed that the duality transformation changes the asymptotic behavior of solutions from $AdS_{3} \times \mathbb{R}$ 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 $\sigma$-models and show that this model describes an exact CFT (equivalent to the $GL(2,\mathbb{R})$ WZW model). After that, the conformal invariance of T-dual models up to two-loop order (first order in $\alpha'$) is discussed.

Simultaneous T-dualization of type II pure spinor superstring

In this article we consider simultaneous T-dualization of the type II superstring action in a pure spinor formulation. Simultaneous T-dualization means that we make T-dualization at the same time along some subset of initial coordinates denoted by x^a. The only imposed assumption stems from the applicability of the Buscher T-dualization procedure—background fields do not depend on the dualized directions x^a. In this way we obtain the full form of the T-dual background fields and T-dual transformation laws. Because the two chiral sectors transform differently, there are two sets of vielbeins and gamma matrices connected by a local Lorentz transformation. Its spinorial representation is the same as in the constant background case. We also found the full expression for the T-dual dilaton field.

Nonrelativistic string theory and T-duality

Nonrelativistic string theory in flat spacetime is described by a two-dimensional quantum field theory with a nonrelativistic global symmetry acting on the worldsheet fields. Nonrelativistic string theory is unitary, ultraviolet complete and has a string spectrum and spacetime S-matrix enjoying nonrelativistic symmetry. The worldsheet theory of nonrelativistic string theory is coupled to a curved spacetime background and to a Kalb-Ramond two-form and dilaton field. The appropriate spacetime geometry for nonrelativistic string theory is dubbed string Newton-Cartan geometry, which is distinct from Riemannian geometry. This defines the sigma model of nonrelativistic string theory describing strings propagating and interacting in curved background fields. We also implement T-duality transformations in the path integral of this sigma model and uncover the spacetime interpretation of T-duality. We show that T-duality along the longitudinal direction of the string Newton-Cartan geometry describes relativistic string theory on a Lorentzian geometry with a compact lightlike isometry, which is otherwise only defined by a subtle infinite boost limit. This relation provides a first principles definition of string theory in the discrete light cone quantization (DLCQ) in an arbitrary background, a quantization that appears in nonperturbative approaches to quantum field theory and string/M-theory, such as in Matrix theory. T-duality along a transverse direction of the string Newton-Cartan geometry equates nonrelativistic string theory in two distinct, T-dual backgrounds.

Open-string T-duality and applications to non-geometric backgrounds

We revisit T-duality transformations for the open string via Buscher’s procedure and work-out technical details which have been missing so far in the literature. We take into account non-trivial topologies of the world-sheet, we consider T-duality along directions with Neumann as well as Dirichlet boundary conditions, and we include collective T-duality along multiple directions.We illustrate this formalism with the example of the three-torus with H-flux and its T-dual backgrounds, and we discuss global properties of open-string boundary conditions on such spaces.

Mesons from (non) Abelian T-dual backgrounds

In this work we study mesonic excitations in a Quantum Field Theory dual to the non Abelian T-dual of AdS5 × S5, using a D6 brane probe on the Sfetsos-Thompson background. Before and after the duality, we observe interesting differences between the spectra and interpret them. The spectrum of masses and the interactions between mesonic excitations teach valuable lessons about the character of non-Abelian T-duality and its implications for Holography. The case of Abelian T-duality is also studied.

Field theory aspects of non-Abelian T-duality and N $$ \mathcal{N} $$ =2 linear quivers

In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS 5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d $$ \mathcal{N} $$ = 2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Nunez. This suggests different completions of the long quiver describing the CFT dual to the nonAbelian T-dual background that match different observables.

Oscillating strings and non-AbelianT-dual Klebanov-Witten background

We study oscillating string solutions in the Klebanov-Witten and its non-Abelian T-dual background dualised along an SU(2) isometry. We find the string energy as the function of oscillation number and angular momentum. We show that for a particular set of T-dual co-ordinates both the background have equal string states. We also study the string states where the strings are expanding and contracting in the T-dual co-ordinate direction. We expect the presence of the superconformal field theory dual operators whose anomalous dimensions depend on T-dual co-ordinate.

Covariant action for a string in doubled yet gauged spacetime

The section condition in double field theory has been shown to imply that a physical point should be one-to-one identified with a gauge orbit in the doubled coordinate space. Here we show the converse is also true, and continue to explore the idea of spacetime being doubled yet gauged. Introducing an appropriate gauge connection, we construct a string action, with an arbitrary generalized metric, which is completely covariant with respect to the coordinate gauge symmetry, generalized diffeomorphisms, world-sheet diffeomorphisms, world-sheet Weyl symmetry and O(D,D) T-duality. A topological term previously proposed in the literature naturally arises and a self-duality condition follows from the equations of motion. Further, the action may couple to a T-dual background where the Riemannian metric becomes everywhere singular.

(Non-)commutative closed string on T-dual toroidal backgrounds

Abstract In this paper we investigate the connection between (non-)geometry and (non-)commutativity of the closed string. To this end, we solve the classical string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted torus and a non-geometric background with Q-flux. In all three situations we work under the assumption of a dilute flux and consider quantities to linear order in the flux density. Furthermore, we perform the first steps of a canonical quantization for the twisted torus, to derive commutators of the string expansion modes. We use them as well as T-duality to determine, in the non-geometric background, a commutator of two string coordinates, which turns out to be non-vanishing. We relate this non-commutativity to the closed string boundary conditions, and the non-geometric Q-flux.

Bounded region with closed time-like curves in T-dual pp-waves backgrounds

Abstract In the 10-dimensional pp-waves background we have found using T-duality a 4-dimensional space-time in which closed time-like curves appear in the region bounded by two coaxial elliptic cylinders. This 4-dimensional space-time is similar to the Gödel-type space-time only in this region. Outside of this region the causal pathology does not appear.

Global aspects of T-duality, gauged sigma models and T-folds

The gauged sigma-model argument that string backgrounds related by T-duality give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.

String vacua with flux from freely-acting obifolds

A precise correspondence between freely-acting orbifolds (Scherk-Schwarz compactifications) and string vacua with NSNS flux turned on is established using T-duality. We focus our attention to a certain non-compact Z_2 heterotic freely-acting orbifold with N=2 supersymmetry (SUSY). The geometric properties of the T-dual background are studied. As expected, the space is non-Kahler with the most generic torsion compatible with SUSY. All equations of motion are satisfied, except the Bianchi identity for the NSNS field, that is satisfied only at leading order in derivatives, i.e. without the curvature term. We point out that this is due to unknown corrections to the standard heterotic T-duality rules.