Vacuum instability in topologically massive gauge theory

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T . We show that such a construction works in the c = −2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra.

Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

Kogan

Nichols

2002

Extended chiral algebras in the SU(2)₀WZNW model

Nichols

2002

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU (2) 0 WZNW model. These have a form almost identical to that found in the c = −2 model but have, in addition, an extended affine Lie algebraic structure. Moreover on Hamiltonian reduction these SU (2) 0 W -algebras exactly reduce to those found in c = −2. We explicitly find the free field representations for the chiral j = 2 and j = 3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j = 2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory. 1 a.nichols1@physics.ox.ac.uk 2 Extended Chiral Algebras Free field representationWe shall use the standard Wakimoto representation [70] for the affine Lie algebra SU(2) specialised to the case k = 0. Our currents are:where β and γ obey the standard free field relations:

Extended multiplet structure in Logarithmic Conformal Field Theories

Nichols¹

2003

We use the process of quantum hamiltonian reduction of SU (2) k , at rational level k, to study explicitly the correlators of the h 1,s fields in the c p,q models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h 1,s operators beyond the 'minimal' sector. At the level of the vacuum null vector h 1,2p−1 = (p − 1)(q − 1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h 1,4p−1 = (2p − 1)(2q − 1). We conjecture that this triplet algebra may produce a rational extended c p,q model. We also find a doublet of fields at h 1,3p−1 = ( 3p 2 − 1)( 3q 2 − 1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic. 1 a.nichols1@physics.ox.ac.uk 2 Knizhnik-Zamolodchikov equationWe consider the SU(2) theory at rational level k. The OPE of the affine Kac-Moody currents is given by: