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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Mr Davide Polvara

Penati, Silvia & Polvara, Davide (2019). Quantum anomalies in Ar(1) Toda theories with defects. Journal of High Energy Physics 2019(6): 62.

Author(s) from Durham


We study quantum integrability of ane Toda theories with a line of defect. In
particular, we focus on the problem of constructing quantum higher-spin conserved currents
in models de ned by two A(1)
r Toda theories separated by a non-trivial type-I defect. For a
suitable choice of the defect potential these theories are known to be classically integrable,
that is they possess an in nite set of higher-spin conserved charges in involution. Studying
the corresponding conservation laws at quantum level we discover that anomalies arise,
which we compute exactly at all orders in the coupling constant. While for the stress-energy
tensor these anomalies can be cancelled by a nite renormalization of the defect potential,
we nd that from the rst non-trivial higher-spin current this is no longer possible. This
opens the question whether these theories are indeed integrable at quantum level.