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An algebraic classification of solution generating techniques

Sep 13, 2021

8 pages

Published in:

Phys.Lett.B 823 (2021) 136771

Published: Dec 10, 2021

e-Print:

2109.06185 [hep-th]

DOI:

10.1016/j.physletb.2021.136771 (publication)

Report number:

MI-HET-762

View in:

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Abstract: (Elsevier B.V.)

We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of 2-dimensional σ-models giving rise to integrable-preserving transformations. Assuming a generalised Scherk-Schwarz ansatz, in fact, the two problems admit essentially the same algebraic formulation, emerging from an underlying double Lie algebra

d

. After presenting our derivation of the classification, we discuss in detail the relation to modified supergravity and the additional conditions to recover the standard (unmodified) supergravity. Starting from our master equation — that encodes all the possible continuous deformations allowed in the family of solution-generating techniques — we show that these are classified by the Lie algebra cohomologies

H^{2} (h, R)

and

H^{3} (h, R)

of the maximally isotropic subalgebra

h

of the double Lie algebra

d

. We illustrate our results with a non-trivial example, the bi-Yang-Baxter-Wess-Zumino model.

Note:

8 pages

algebra: Lie
transformation: canonical
supergravity
deformation
master equation
integrability
sigma model
Yang-Baxter
mathematical methods

References(48)

Figures(0)

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