$\lambda$-Deformations in the upper-half plane

Sfetsos, Konstantinos; Siampos, Konstantinos

doi:10.1016/j.nuclphysb.2021.115451

$\lambda$ -Deformations in the upper-half plane

Konstantinos Sfetsos
(
- Athens U.
)
,
Konstantinos Siampos
(
- Athens U.
)

Mar 15, 2021

69 pages

Published in:

Nucl.Phys.B 968 (2021) 115451

Published: Jul, 2021

e-Print:

2103.08650 [hep-th]

DOI:

10.1016/j.nuclphysb.2021.115451 (publication)

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Abstract: (Elsevier)

We formulate λ -deformed σ -models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter λ and for large values of the level k of the underlying WZW model. To perform our computations we use either conformal perturbation theory in association with Cardy's doubling trick, as well as meromorphicity arguments and a non-perturbative symmetry in the parameter space (λ,k) , or standard QFT techniques based on the free field expansion of the σ -model action, with the free fields obeying appropriate boundary conditions. Both methods have their own advantages yielding consistent and rich, compared to those in the absence of a boundary, complementary results. We pay particular attention, albeit not exclusively, to integrability preserving boundary conditions.

Note:

v1: 45 pages + 24 pages appendices, v2: NPB version

operator: primary
boundary condition
field theory
Wess-Zumino-Witten model
correlation function
perturbation theory
nonperturbative
integrability
deformation
conformal

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