Polylogarithm identities in a conformal field theory in three-dimensions - INSPIRE

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Polylogarithm identities in a conformal field theory in three-dimensions

Subir Sachdev
(
- Yale U.
)

Jun 7, 1993

7 pages

Published in:

Phys.Lett.B 309 (1993) 285-288

e-Print:

hep-th/9305131 [hep-th]

DOI:

10.1016/0370-2693(93)90935-B

Report number:

PRINT-93-0431 (YALE)

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Abstract:

The

N=\infty

vector

O(N)

model is a solvable, interacting field theory in three dimensions (

D

). In a recent paper with A. Chubukov and J. Ye\cite{self}, we have computed a universal number,

\tilde{c}

, characterizing the size dependence of the free energy at the conformally-invariant critical point of this theory. The result\cite{self} for

\tilde{c}

can be expressed in terms of polylogarithms. Here, we use non-trivial polylogarithm identities to show that

\tilde{c}/N = 4/5

, a rational number; this result is curiously parallel to recent work on dilogarithm identities in

D=2

conformal theories. The amplitude of the stress-stress correlator of this theory,

c

(which is the analog of the central charge), is determined to be

c/N=3/4

, also rational. Unitary conformal theories in

D=2

always have

c = \tilde{c}

; thus such a result is clearly not valid in

D=3

.

field theory: conformal
dimension: 3
model: vector
symmetry: O(N)
correlation function
regularization: dimensional
critical phenomena

References(13)

Figures(0)

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