D-branes in λ-deformations

We invent a method that exploits the geometry in the space of couplings and the known all-loop effective action, in order to calculate the exact in the couplings anomalous dimensions of composite operators for a wide class of integrable σ-models. These involve both self and mutually interacting current algebra theories. We work out the details for important classes of such operators. In particular, we consider the operators built solely from an arbitrary number of currents of the same chirality, the composite operators which factorize into a chiral and an anti-chiral part, as well as those made up of three currents of mixed chirality. Remarkably enough, the anomalous dimensions of the former two sets of operators turn out to vanish. In our approach, loop computations are completely avoided.

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“…Remarkably, in these λ-deformed σ-models the computation of Zamolodchikov's the context of single λ-deformations were studied in [50,6].…”

Section: Introductionmentioning

confidence: 99%

Exact results from the geometry of couplings and the effective action

et al. 2019

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“…The method consists of demanding that a monodromy matrix constructed from a Lax connection generates an infinite tower of conserved non-local charges when a boundary is present 1 . We will briefly review it here, following [10,1], as well as the case without boundaries to introduce notations.…”

Section: The Boundary Monodromy Methods For Integrable Systemsmentioning

confidence: 99%

“…Hence, the deformation of the WZW group manifold can be thought of as a bosonic trunctation of a truly superstring theory. The question of establishing D-branes in this deformed geometry is therefore natural and has been pursued in the article [1] on which this proceedings is based. We will see, by demanding integrability, that the geometrical picture of twisted conjugacy classes of the WZW point persists and naturally fits in the deformed geometry.…”

Section: Introductionmentioning

confidence: 99%

“…The semi-classical flux quantisation will turn out to consistently be independent of the continuous λdeformation parameter. Additionally the λ -deformation allows to track the behaviour of D-branes under generalised dualities [1] -again a challenging question in general curved backgrounds-by the non-Abelian T-dual scaling limit and Poisson-Lie T-duality to the integrable η-deformation of the PCM [18,19,20]. Illustrated for the G = SU(2) manifold one will find under both dualities D2-branes transforming to space-filling D3-branes that can be shown to preserve the classical integrable structure of the dual theories.…”

Section: Introductionmentioning

confidence: 99%

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Open strings in integrable deformations of sigma models

Driezen¹

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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“…An obvious question to ask is: viewing the λ -model as a deformation of the WZW can we identify D-brane configurations for which integrability persists? The technique used in [206] was to find conditions such that a monodromy object T b (z) formed by taking the Wilson line of the Lax to the boundary and reflecting back, obeys ∂ τ T b (z) = [T b (z), N] for some matrix N and such that Tr T b (z) generates conserved charges. For the λ -model this is the case when…”

Section: Boundaries and D-branesmentioning

confidence: 99%

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

Thompson¹

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications. We explain how each of these has seen recent application in the context of holography. Non-Abelian T-duality has been used to construct new holographic dual geometries. Poisson-Lie duality has been used to construct new integrable string sigma-models including the η-and λ -deformations of the AdS 5 × S 5 superstring thought to encode quantum group deformations of holography. We also comment on the doubled worldsheet description that makes such dualities manifest. duality serves to interchange a conservation law, that associated to the U(1) global symmetry of the compact boson θ of radius R, with the Bianchi identity for the dual bosonθ :( 1.3) Just as with bosonisation the connection between the two variables involves derivatives, i.e. the map between variables is a non-local one. Also akin to the Abelian bosonisation, the dual theory can be established through an analogous path integral manipulation 1 known as the Buscher procedure [22,23]. Given the close analogy between T-duality and Abelian bosonisation one might wonder if there is a T-duality equivalent to non-Abelian bosonisation. More specifically, in string theory we are immediately prompted to ask if there is an extension of T-duality to the case of a non-Abelian set of isometries, or even if there are still more exotic notions of T-duality? A secondary question is then, if such dualities exist, what are they useful for? The remainder of these lectures seek to outline some answers to these two questions.Our journey will involve exploring a hierarchy of possible dualities in the following string theory scenarios:

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D-branes in λ-deformations

Cited by 24 publications

References 88 publications

Exact results from the geometry of couplings and the effective action

Exact results from the geometry of couplings and the effective action

Open strings in integrable deformations of sigma models

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

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