Abstract
The classical spectral curve for the worldsheet theory of the AdS5×S5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T-dual of the AdS5×S5 superstring with respect to the full PSU(2, 2|4) symmetry. The form of the curve is identified as the semi-classical limit of a set of Bethe ansatz equations for an XXZ type spin chain for the supergroup PSU(2, 2|4) in contrast to the string in AdS5×S5 which is XXX type.
Highlights
A fascinating integrable system is the world-sheet theory of the string in AdS5×S5 and the N = 4 gauge-gravity duality.1 In this case, the form of the classical curve has been determined in [4]
The curve is determined by the solution of some auxiliary integral equations that can be viewed as a complicated Riemann-Hilbert problem
The Asymptotic Bethe Ansatz (ABA) can be viewed as a direct quantization of the classical spectral curve and it had a direct connection to the dual gauge theory
Summary
The world-sheet theories of the conventional AdS5×S5 superstring and lambda deformation involve the semi-symmetric space F/G = PSU(2, 2|4)/Sp(2, 2) × Sp(4), whose bosonic part is precisely AdS5×S5 realised as the product of symmetric spaces SU(2, 2)/Sp(2, 2) × SU(4)/Sp(4). Our conventions for this superalgebra are taken from [3]. The generators are matrices EAB with a 1 in position (A, B) and zeros elsewhere. The c-parity determines the reality condition on the generators by specifying an anti-linear conjugation of the form.
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