Searcharxiv⌕ Search

arXiv subjects

Daniel C. Thompson

Publications and source records attributed to Daniel C. Thompson.

At least 37 records · Page 2Linked to original sources
arXiv2018

Doubled aspects of generalised dualities and integrable deformations

The worldsheet theories that describe Poisson-Lie T-dualisable $σ$-models on group manifolds as well as integrable $η$, $λ$ and $β$-deformations provide examples of ${\cal E}$-models. Here we show how such ${\cal E}$-models can be given an elegant target space description within Double Field Theory by specifying explicitly generalised frame fields forming an algebra under the generalised Lie derivative. With this framework we can extract simple criteria for the R/R fields and the dilaton that extend the ${\cal E}$-model conditions to type II backgrounds. In particular this gives conditions for a type II background to be Poisson-Lie T-dualisable. Our approach gives rise to algebraic field equations for Poisson-Lie symmetric spacetimes and provides an effective tool for their study.

hep-th↗
arXiv2018

D-branes in $λ$-deformations

We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the $λ$--deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the $λ$--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 $SU(2)$ and $SL(2,\mathbb{R})$, 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 $λ$--deformed theory map, under analytic continuation together with Poisson-Lie T-duality, to D3 branes in the $η$-deformation of the principal chiral model.

hep-th↗
arXiv2018

Quantum Anisotropic Sigma and Lambda Models as Spin Chains

We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ Heisenberg chain and can be solved by using the Bethe Ansatz. This yields the spectrum and S-matrix of the excitations. In particular, we find the S-matrix in the gapped anti-ferromagnetic regime. In this regime, a continuum limit does not exist and this suggests that the field theories in this regime, precisely ones with a cyclic RG like the Yang-Baxter deformations, may only exist as effective theories. In a certain limit, we show that the XXZ type lambda model gives the symmetric space SU(2)/U(1) lambda model and, hence, we are able to find its spectrum and S-matrix and show that it gives the S-matrix of the O(3) sigma model in the appropriate limit. Finally, we show the full consistency of the S-matrix and the Lagrangian formulations of the lambda model, by coupling to a conserved charge and computing the way the ground state energy changes in both pictures.

hep-th↗
arXiv2018

Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds

We show that the string worldsheet theory of Gaiotto-Maldacena holographic duals to N=2 superconformal field theories generically fails to be classically integrable. We demonstrate numerically that the dynamics of a winding string configuration possesses a non-vanishing Lyapunov exponent. Furthermore an analytic study of the Normal Variational Equation fails to yield a Liouvillian solution. An exception to the generic non-integrability of such backgrounds is provided by the non-Abelian T-dual of $AdS_5 \times S^5$. Here by virtue of the canonical transformation nature of the T-duality classical integrability is known to be present.

hep-th↗
arXiv2018

O-folds: Orientifolds and Orbifolds in Exceptional Field Theory

We describe conventional orientifold and orbifold quotients of string and M-theory in a unified approach based on exceptional field theory (ExFT). Using an extended spacetime, ExFT combines all the maximal ten and eleven dimensional supergravities into a single theory manifesting a global symmetry corresponding to the exceptional series of Lie groups. Here we will see how this extends to half-maximal theories by showing how a single $\mathbb{Z}_2$ generalised orbifold (or O-fold) of ExFT gives rise to M-theory on an interval, type II with orientifold planes and the heterotic theories in an elegant fashion. We study in more detail such orbifold and orientifold actions preserving half-maximal supersymmetry, and show how the half-maximal structure of ExFT permits the inclusion of localised non-Abelian vector multiplets located at the orbifold fixed points. This allows us to reproduce for the $\mathbb{Z}_2$ example the expected modifications to the gauge transformations, Bianchi identities and actions of the theories obtained from the single ExFT starting point. We comment on the prospects of studying anomaly cancellation and more complicated, non-perturbative O-folds in the ExFT framework.

hep-th↗
arXiv2018

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 beta 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.

hep-th↗
arXiv2017

Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices

Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.

hep-th↗
arXiv2016

Marginal and non-commutative deformations via non-abelian T-duality

In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-$β$-deformations and non-commutative deformations of ${\cal N}=4$ super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.

hep-th↗
arXiv2016

Aspects of the Doubled Worldsheet

We clarify the relation between various approaches to the manifestly T-duality symmetric string. We explain in detail how the PST covariant doubled string arises from an unusual gauge fixing. We pay careful attention to the role of "spectator" fields in this process and also show how the T-duality invariant doubled dilaton emerges naturally. We extend these ideas to non-Abelian T-duality and show they give rise to the duality invariant formalism based on the semi-Abelian Drinfeld Double. We then develop the N=(0,1) supersymmetric duality invariant formalism.

hep-th↗
arXiv2016

Resurgence in $η$-deformed Principal Chiral Models

We study the $SU(2)$ Principal Chiral Model (PCM) in the presence of an integrable $η$-deformation. We put the theory on $\mathbb{R}\times S^1$ with twisted boundary conditions and then reduce the circle to obtain an effective quantum mechanics associated with the Whittaker-Hill equation. Using resurgent analysis we study the large order behaviour of perturbation theory and recover the fracton events responsible for IR renormalons. The fractons are modified from the standard PCM due to the presence of this $η$-deformation but they are still the constituents of uniton-like solutions in the deformed quantum field theory. We also find novel $SL(2,\mathbb{C})$ saddles, thus strengthening the conjecture that the semi-classical expansion of the path integral gives rise to a resurgent transseries once written as a sum over Lefschetz thimbles living in a complexification of the field space. We conclude by connecting our quantum mechanics to a massive deformation of the $\mathcal{N}=2~$ $4$-d gauge theory with gauge group $SU(2)$ and $N_f=2$.

hep-th↗
arXiv2015

Holographic Flows in non-Abelian T-dual Geometries

We use non-Abelian T-duality to construct new N=1 solutions of type IIA supergravity (and their M-theory lifts) that interpolate between AdS_5 geometries. We initiate a study of the holographic interpretation of these backgrounds as RG flows between conformal fixed points. Along the way we give an elegant formulation of non-Abelian T-duality when acting on a wide class of backgrounds, including those corresponding to such flows, in terms of their SU(2) structure.

hep-th↗
arXiv2015

Generalised integrable $λ$- and $η$-deformations and their relation

We construct two-parameter families of integrable $λ$-deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric coset space. In examples based on the $SU(2)$ WZW model and the $SU(2)/U(1)$ exact coset CFT, we show that these deformations are related to bi-Yang-Baxter generalisations of $η$-deformations via Poisson-Lie T-duality and analytic continuation. We illustrate the quantum behaviour of our models under RG flow. As a byproduct we demonstrate that the bi-Yang-Baxter $σ$-model for a general group is one-loop renormalisable.

hep-th↗
arXiv2015

Integrable $λ$-deformations: Squashing Coset CFTs and $AdS_5\times S^5$

We examine integrable $λ$-deformations of $SO(n+1)/SO(n)$ coset CFTs and their analytic continuations. We provide an interpretation of the deformation as a squashing of the corresponding coset $σ$-model's target space. We realise the $λ$-deformation for $n=5$ case as a solution to supergravity supported by non-vanishing five-form and dilaton. This interpolates between the coset CFT $SO(4,2)/SO(4,1)\times SO(6)/SO(5)$ constructed as a gauged WZW model and the non-Abelian T-dual of the $AdS_5\times S^5$ spacetime.

hep-th↗
arXiv2014

Duality Symmetric String and M-Theory

We review recent developments in duality symmetric string theory. We begin with the world sheet doubled formalism which describes strings in an extended space time with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an E_{n(n)} U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extend space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.

hep-th↗
arXiv2014

Spacetimes for λ-deformations

We examine a recently proposed class of integrable deformations to two-dimensional conformal field theories. These λ-deformations interpolate between a WZW model and the non-Abelian T-dual of a Principal Chiral Model on a group G or, between a G/H gauged WZW model and the non-Abelian T-dual of the geometric coset G/H. λ-deformations have been conjectured to represent quantum group q-deformations for the case where the deformation parameter is a root of unity. In this work we show how such deformations can be given an embedding as full string backgrounds whose target spaces satisfy the equations of type-II supergravity. One illustrative example is a deformation of the Sl(2,R)/U(1) black-hole CFT. A further example interpolates between the $\frac{SU(2)\times SU(2)}{SU(2)}\times\frac{SL(2,R)\times SL(2,R)}{SL(2,R)} \times U(1)^4$ gauged WZW model and the non-Abelian T-dual of $AdS_3\times S^3\times T^4$ supported with Ramond flux.

hep-th↗
arXiv2014

New ${\cal N} = 1$ supersymmetric $AdS_5$ backgrounds in Type IIA supergravity

We present a family of N=1 supersymmetric backgrounds in type-IIA supergravity and their lifts to eleven-dimensional supergravity. These are of the form $AdS_5 \times X^5$ and are characterised by an $SU(2)$ structure. The internal space, $X^5$, is obtained from the known Sasaki-Einstein manifolds, $Y^{p,q}$, via an application of non-Abelian T-duality.

hep-th↗
arXiv2013

Dualising the Baryonic Branch: Dynamic SU(2) and confining backgrounds in IIA

In this paper we construct and examine new supersymmetric solutions of massive IIA supergravity that are obtained using non-Abelian T-duality applied to the Baryonic Branch of the Klebanov-Strassler background. The geometries display SU(2) structure which we show flows from static in the UV to dynamical in the IR. Confinement and symmetry breaking are given a geometrical interpretation by this change of structure. Various field theory observables are studied, suggesting possible ways to break conformality and flow in $N=1$ $T_N$ and related field theories.

hep-th↗