Abstract
Lie algebra expansion is a technique to generate new Lie algebras from a given one. In this paper, we apply the method of Lie algebra expansion to superstring σ-models with a ℤ4 coset target space. By applying the Lie algebra expansion to the isometry algebra, we obtain different σ-models, where the number of dynamical fields can change. We reproduce and extend in a systematic way actions of some known string regimes (flat space, BMN and non-relativistic in AdS5×S5). We define a criterion for the algebra truncation such that the equations of motion of the expanded action of the new σ-model are equivalent to the vanishing curvature condition of the Lax connection obtained by expanding the Lax connection of the initial model.
Highlights
There has been a remarkable effort in investigating the integrable AdSd/CFTd−1 duality, with d < 5, and integrable deformations, [2, 3, 5,6,7,8], see references therein
We apply the method of Lie algebra expansion to superstring σ-models with a Z4 coset target space
One of the powerful features of the Lie algebra expansion is that it comes equipped with the so-called truncation rules, which ensure that the expansion is truncated consistently
Summary
We denote Maurer-Cartan 1-forms with calligraphic letters, and Lie algebra generators with latin uppercase letters. With the convention defined in eq (A.1), where ‘str’ stands for the inner product on g, M3 is a 3-dimensional manifold, whose boundary is the 2-dimensional string world-sheet, and the brackets between the currents in the Wess-Zumino term of eq (2.9) indicate that the (anti)commutator between the generators must be taken. The relative coefficient between the kinetic and the Wess-Zumino terms in eq (2.9) is fixed to be ±1 by requiring invariance of the full action under κ-symmetry [60]. Having described the σ-model and some aspects of its classical integrability, we shall introduce the Lie algebra expansion method
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