Η-deformed AdS5 Research Articles

Quantum spectral curve for the η-deformed AdS5 × S5 superstring

The spectral problem for the AdS5×S5 superstring and its dual planar maximally supersymmetric Yang–Mills theory can be efficiently solved through a set of functional equations known as the quantum spectral curve. We discuss how the same concepts apply to the η-deformed AdS5×S5 superstring, an integrable deformation of the AdS5×S5 superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS5×S5 superstring, like the relation between the XXZ and XXX spin chains, or the sausage and the S2 sigma models for instance. We derive the quantum spectral curve for the η-deformed string by reformulating the corresponding ground-state thermodynamic Bethe ansatz equations as an analytic Y system, and map this to an analytic T system which upon suitable gauge fixing leads to a Pμ system – the quantum spectral curve. We then discuss constraints on the asymptotics of this system to single out particular excited states. At the spectral level the η-deformed string and its quantum spectral curve interpolate between the AdS5×S5 superstring and a superstring on “mirror” AdS5×S5, reflecting a more general relationship between the spectral and thermodynamic data of the η-deformed string. In particular, the spectral problem of the mirror AdS5×S5 string, and the thermodynamics of the undeformed AdS5×S5 string, are described by a second rational limit of our trigonometric quantum spectral curve, distinct from the regular undeformed limit.

Generalized IIB supergravity from exceptional field theory

The background underlying the η-deformed AdS5 × S5 sigma-model is known to satisfy a generalization of the IIB supergravity equations. Their solutions are related by T-duality to solutions of type IIA supergravity with non-isometric linear dilaton. We show how the generalized IIB supergravity equations can be naturally obtained from exceptional field theory. Within this manifestly duality covariant formulation of maximal supergravity, the generalized IIB supergravity equations emerge upon imposing on the fields a simple Scherk-Schwarz ansatz which respects the section constraint.

Some three-point correlation functions in the η-deformed AdS5 × S5

We compute some normalized structure constants in the [Formula: see text]-deformed [Formula: see text] in the framework of the semiclassical approach. This is done for the cases when the “heavy” string states are finite-size giant magnons carrying one angular momentum and for three different choices of the “light” state: primary scalar operators, dilaton operator with nonzero momentum, singlet scalar operators on higher string levels. Since the dual field theory is still unknown, the results obtained here must be considered as conjectures or as predictions from the string theory side.

Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations

We consider the ABF background underlying the η-deformed AdS5×S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η-deformed model is scale invariant. This property follows from the formal relation via T-duality between the η-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R–R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R–R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, they imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS3×S3×T4and AdS2×S2×T6models.

Type IIB supergravity solution for the T-dual of the η-deformed AdS 5 × S 5 superstring

We find an exact type IIB supergravity solution that represents a one-parameter deformation of the T-dual of the AdS 5 × S 5 background (with T-duality applied in all 6 abelian bosonic isometric directions). The non-trivial fields are the metric, dilaton and RR 5-form only. The latter has remarkably simple “undeformed” form when written in terms of a “deformation-rotated” vielbein basis. An unusual feature of this solution is that the dilaton contains a linear dependence on the isometric coordinates of the metric precluding a straightforward reversal of T-duality. If we still formally dualize back, we find exactly the metric, B-field and product of dilaton with RR field strengths as recently extracted from the η-deformed AdS 5 × S 5 superstring action in arXiv:1507.04239 . We also discuss similar solutions for deformed AdS n × S n backgrounds with n = 2, 3. In the η → i limit we demonstrate that all these backgrounds can be interpreted as special limits of gauged WZW models and are also related to (a limit of) the Pohlmeyer-reduced models of the AdS n × S n superstrings.

On the asymptotic states and the quantum S matrix of the η-deformed AdS5 × S5 superstring

We investigate the worldsheet S matrix of string theory in η-deformed AdS5×S5. By computing the six-point tree-level S matrix we explicitly show that there is no particle production at this level, ...

An HHL 3-point correlation function in the η-deformed AdS5 × S5

We derive the 3-point correlation function between two giant magnons heavy string states and the light dilaton operator with zero momentum in the η-deformed AdS5×S5 valid for any J1 and η in the semiclassical limit. We show that this result satisfies a consistency relation between the 3-point correlation function and the conformal dimension of the giant magnon. We also provide a leading finite J1 correction explicitly.

The exact spectrum and mirror duality of the (AdS5 × S 5) η superstring

We discuss the spectrum of a string propagating on η-deformed AdS5 × S5 by treating its worldsheet theory as an integrable quantum field theory. The exact S-matrix of this field theory is given by a qdeformation of the AdS5 × S5 worldsheet S-matrix with a real deformation parameter. By considering mirror (double Wick-rotated) versions of these worldsheet theories, we give the thermodynamic Bethe ansatz description of their exact finite-size spectra. Interestingly, this class of models maps onto itself under the mirror transformation. At the string level, this seems to indicate that the light-cone worldsheet theories of strings on particular pairs of backgrounds are related by a double Wick rotation, a feature we call “mirror duality.” We provide a partial verification of these statements at the level of a sigma model by considering reduced actions and their corresponding (mirror) giant magnon solutions.

Finite-size giant magnons on η-deformed [formula omitted

We consider strings moving in the Rt×Sη3 subspace of the η-deformed AdS5×S5 and obtain a class of solutions depending on several parameters. They are characterized by the string energy and two angular momenta. Finite-size dyonic giant magnon belongs to this class of solutions. Further on, we restrict ourselves to the case of giant magnon with one nonzero angular momentum, and obtain the leading finite-size correction to the dispersion relation.

S-matrix for strings on η-deformed AdS5 × S5

We determine the bosonic part of the superstring sigma model Lagrangian on η-deformed AdS5 × S5, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of the model. We then compare it with the large string tension limit of the q-deformed S-matrix and find exact agreement.