15 research outputs found
Supergravity solution-generating techniques and canonical transformations of σ-models from O(D, D)
Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant generalised fluxes interpreted as gaugings. We analyse the various possibilities of turning on the fluxes Hijk, Fijk, Qijk and Rijk, and the solutions for the twists allowed in each case. While we do not impose the DFT (or equivalently supergravity) equations of motion, our results provide solution-generating techniques in supergravity when applied to a background that does solve the DFT equations. At the same time, our results give rise also to canonical transformations of 2-dimensional σ-models, a fact which is interesting especially because these are integrability-preserving transformations on the worldsheet. Both the solution-generating techniques of supergravity and the canonical transformations of 2-dimensional σ-models arise as maps that leave the generalised fluxes of DFT and their flat derivatives invariant. These maps include the known abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter deformations, as well as novel generalisations of themS
Integrable asymmetric λ-deformations
We construct integrable deformations of the -type for asymmetrically
gauged WZW models. This is achieved by a modification of the Sfetsos gauging
procedure to account for a possible automorphism that is allowed in
models. We verify classical integrability, derive the one-loop beta function
for the deformation parameter and give the construction of integrable D-brane
configurations in these models. As an application, we detail the case of the
-deformation of the cigar geometry corresponding to the axial gauged
theory at large . Here we also exhibit a range of both A-type
and B-type integrability preserving D-brane configurations.Comment: 25 pages, 1 figur
Exact approaches on the string worldsheet
We review different exact approaches to string theory. In the context of the
Green-Schwarz superstring, we discuss the action in curved backgrounds and its
supercoset formulation, with particular attention to superstring backgrounds of
the type supported by both Ramond-Ramond and
Neveu-Schwarz-Neveu-Schwarz fluxes. This is the basis for the discussion of
classical integrability, of worldsheet-scattering factorisation in the uniform
lightcone gauge, and eventually of the string spectrum through the mirror
thermodynamic Bethe ansatz, which for backgrounds was only derived and
analysed very recently. We then illustrate some aspects of the
Ramond-Neveu-Schwarz string, and introduce the formalism of
Berkovits-Vafa-Witten, which has seen very recent applications to
physics, which we also briefly review. Finally, we present the relation between
M-theory in the discrete lightcone quantisation and decoupling limits of string
theory that exhibit non-relativistic behaviours, highlighting the connection
with integrable deformations, as well as the relation between
spin-matrix theory and Landau-Lifshitz models. This review is based on lectures
given at the Young Researchers Integrability School and Workshop 2022 "Taming
the string worldsheet" at NORDITA, Stockholm.Comment: 283 pages; v2: references adde
Classical and quantum aspects of Yang-Baxter Wess-Zumino models
We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term. For arbitrary groups, the one-loop -functions are calculated and display a surprising connection between classical and quantum physics: the classical integrability condition is necessary to prevent new couplings being generated by renormalisation. We show these theories admit an elegant realisation of Poisson-Lie T-duality acting as a simple inversion of coupling constants. The self-dual point corresponds to the Wess-Zumino-Witten model and is the IR fixed point under RG. We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general
D-branes in λ-deformations
We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the --deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the --deformed theory continues to produce conserved charges in the presence of boundaries. In this way the D-brane configurations obtained correspond to ``integrable'' boundary configurations. We illustrate this with examples based on and , and comment on the relation of these D-branes to both non-Abelian T-duality and Poisson-Lie T-duality. We show that the D2 supported by D0 charge in the --deformed theory map, under analytic continuation together with Poisson-Lie T-duality, to D3 branes in the -deformation of the principal chiral model
Supergravity solution-generating techniques and canonical transformations of -models from
Within the framework of the flux formulation of Double Field Theory (DFT) we
employ a generalised Scherk-Schwarz ansatz and discuss the classification of
the twists that in the presence of the strong constraint give rise to constant
generalised fluxes interpreted as gaugings. We analyse the various
possibilities of turning on the fluxes and
, and the solutions for the twists allowed in each case. While we do
not impose the DFT (or equivalently supergravity) equations of motion, our
results provide solution-generating techniques in supergravity when applied to
a background that does solve the DFT equations. At the same time, our results
give rise also to canonical transformations of 2-dimensional -models, a
fact which is interesting especially because these are integrability-preserving
transformations on the worldsheet. Both the solution-generating techniques of
supergravity and the canonical transformations of 2-dimensional -models
arise as maps that leave the generalised fluxes of DFT and their flat
derivatives invariant. These maps include the known
abelian/non-abelian/Poisson-Lie T-duality transformations, Yang-Baxter
deformations, as well as novel generalisations of them.Comment: 58 pages, 1 figure, 6 appendice