General properties of the boundary renormalization group flow for supersymmetric systems in 1 + 1 dimensions

Daniel Friedan, Anatoly Konechny

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider the general supersymmetric one-dimensional quantum system with boundary, critical in the bulk but not at the boundary. The renormalization group (RG) flow on the space of boundary conditions is generated by the boundary beta functions ßa(?) for the boundary coupling constants ?a. We prove a gradient formula ? ln z/??a = -gSabßb where z(?) is the boundary partition function at given temperature T = 1/ß, and gSab(?) is a certain positive-definite metric on the space of supersymmetric boundary conditions. The proof depends on canonical ultraviolet behavior at the boundary. Any system whose short distance behavior is governed by a fixed point satisfies this requirement. The gradient formula implies that the boundary energy, -? ln z/?ß = - Tßa?a ln z, is nonnegative. Equivalently, the quantity ln z(?) decreases under the RG flow. © 2009 International Press.

Original languageEnglish
Pages (from-to)1847-1874
Number of pages28
JournalAdvances in Theoretical and Mathematical Physics
Volume13
Issue number6
Publication statusPublished - Dec 2009

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