TY - JOUR

T1 - Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

AU - Valach, Fridrich

AU - Youmans, Donald R.

N1 - Publisher Copyright:
© 2020, The Author(s).

PY - 2020/12

Y1 - 2020/12

N2 - We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

AB - We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

KW - Field Theories in Lower Dimensions

KW - Nonperturbative Effects

KW - Topological Field Theories

UR - http://www.scopus.com/inward/record.url?scp=85107334886&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2020)189

DO - 10.1007/JHEP12(2020)189

M3 - Article

AN - SCOPUS:85107334886

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics (JHEP)

JF - Journal of High Energy Physics (JHEP)

IS - 12

M1 - 189

ER -