Integrable sigma models and 2-loop RG flow

We consider λ-deformed current algebra CFTs at level k, interpolating between an exact CFT in the UV and a PCM in the IR. By employing gravitational techniques, we derive the two-loop, in the large k expansion, β-function. We find that this is covariant under a remarkable exact symmetry involving the coupling λ, the level k and the adjoint quadratic Casimir of the group. Using this symmetry and CFT techniques, we are able to compute the Zamolodchikov metric, the anomalous dimension of the bilinear operator and the Zamolodchikov C-function at two-loops in the large k expansion, as exact functions of the deformation parameter. Finally, we extend the above results to λ-deformed parafermionic algebra coset CFTs which interpolate between exact coset CFTs in the UV and a symmetric coset space in the IR.

Section: Discussionsupporting

confidence: 64%

“…September 2019) [26] and at the 10 th Crete regional meeting in String Theory (Kolymbari, Greece, 15-22 September 2019) [27]. Towards the completion of the present work, the work of [28] appeared where similar issues concerning the two-loop β-function in λ-deformed models, are discussed.…”

Section: Note Addedmentioning

confidence: 99%

An exact symmetry in λ-deformed CFTs

Georgiou

Sagkrioti

Sfetsos

et al. 2020

“…With the structure constants related by (4.8), we can derive the following three equations 2 Here EA I has the natural weight 3 5 .…”

Section: The Frame Fields and Embedding Tensormentioning

confidence: 99%

“…Non-Abelian T-duality [1] is a proposed dualisation of closed-string non-linear sigma-models (NLSM) whose target space admits the action of non-Abelian isometry group. Whilst the status of Non-Abelian T-duality in terms of the string genus expansion remains unclear, recent evidence [2] at two-loops provides confidence that the duality could remain robust to quantum (α ′ ) corrections on the worldsheet. What is absolutely clear is that in the context of holography at large N , where both string genus and α ′ corrections are suppressed, Non-Abelian T-duality can be a powerful solution generating technique as advocated first in [3][4][5][6] (see [7] for a review and further references) .…”

Section: Introductionmentioning

confidence: 99%

Poisson-Lie U-duality in exceptional field theory

Malek

Thompson

2020

Poisson-Lie duality provides an algebraic extension of conventional Abelian and non-Abelian target space dualities of string theory and has seen recent applications in constructing quantum group deformations of holography. Here we demonstrate a natural upgrading of Poisson-Lie to the context of M-theory using the tools of exceptional field theory. In particular, we propose how the underlying idea of a Drinfeld double can be generalised to an algebra we call an exceptional Drinfeld algebra. These admit a notion of "maximally isotropic subalgebras" and we show how to define a generalised Scherk-Schwarz truncation on the associated group manifold to such a subalgebra. This allows us to define a notion of Poisson-Lie U-duality. Moreover, the closure conditions of the exceptional Drinfeld algebra define natural analogues of the cocycle and co-Jacobi conditions arising in Drinfeld double. We show that upon making a further coboundary restriction to the cocycle that an M-theoretic extension of Yang-Baxter deformations arise. We remark on the application of this construction as a solution-generating technique within supergravity.

“…Furthermore the correction to the background fields can be cast in a relatively simple form, giving hope that the result can be extended to all orders in the deformation parameter and perhaps higher orders in α ′ .Since the homogeneous YB deformations can be constructed using NATD, our results indicate that also NATD should preserve conformality at two loops, and possibly all orders in α ′ . Another piece of evidence for this comes from the recent analysis of renormalizability of deformed sigma models with two-dimensional target space in [28], and very recently [29]. Some of the deformations considered have a limit where they reduce to NATD and it was found that the models behave nicely beyond lowest order in α ′ suggesting that things should work out to all orders in α ′ .For YB deformations of TsT-type we can also exploit another method to obtain explicit α ′ -corrections and to promote those backgrounds to two-loop solutions.…”

mentioning

confidence: 99%

Two-loop conformal invariance for Yang-Baxter deformed strings

Borsato

Wulff

2020

The so-called homogeneous Yang-Baxter (YB) deformations can be considered a non-abelian generalization of T-duality-shift-T-duality (TsT) transformations. TsT transformations are known to preserve conformal symmetry to all orders in α ′ . Here we argue that (unimodular) YB deformations of a bosonic string also preserve conformal symmetry, at least to two-loop order. We do this by showing that, starting from a background with no NSNS-flux, the deformed background solves the α ′ -corrected supergravity equations to second order in the deformation parameter. At the same time we determine the required α ′ -corrections of the deformed background, which take a relatively simple form. In examples that can be constructed using, possibly non-commuting sequences of, TsT transformations we show how to obtain the first α ′ -correction to all orders in the deformation parameter by making use of the α ′ -corrected T-duality rules. We demonstrate this on the specific example of YB deformations of a Bianchi type II background. sigma model with isometries. This was carried out for the Green-Schwarz superstring in [14] and rules for writing the supergravity background directly in terms of the R-matrix were derived. 2The simplest class of such YB deformations is when R is defined on an abelian subalgebra of the isometry algebra. In this case the deformation is equivalent to a T-duality-shift-T-duality (TsT) transformation [17]. These are also known as O(d, d)-transformations [18,19] and they have been argued to map a consistent string background to another consistent string background, i.e. there should exist corrections to the background fields such that the corrected background solves the α ′ -corrected supergravity equations to all orders in α ′ [20,21,22,23,24,25]. 3 Here we want to ask what happens for YB deformations in general at the quantum level. 4 Unimodular YB deformations are known to give a conformal theory at one loop, i.e. the background solves the (super)gravity equations. Here we will analyze the two-loop equations in the bosonic string case. For simplicity we will restrict to deformations of backgrounds with vanishing NSNS-flux. We will show, to second order in the deformation parameter, that the deformed background can be corrected so that it solves the 2-loop equations. Furthermore the correction to the background fields can be cast in a relatively simple form, giving hope that the result can be extended to all orders in the deformation parameter and perhaps higher orders in α ′ .Since the homogeneous YB deformations can be constructed using NATD, our results indicate that also NATD should preserve conformality at two loops, and possibly all orders in α ′ . Another piece of evidence for this comes from the recent analysis of renormalizability of deformed sigma models with two-dimensional target space in [28], and very recently [29]. Some of the deformations considered have a limit where they reduce to NATD and it was found that the models behave nicely beyond lowest order in α ′ suggesting that things should wor...