Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

Kogan, Ian I.; Nichols, A.

doi:10.1088/1126-6708/2002/01/029

Cited by 25 publications

(45 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In some "well-behaved" cases, the occurrence of the Kazhdan-Lusztigdual quantum group can be seen by taking ι d ι P ι , a direct sum of projective W-modules with some multiplicities d ι chosen such that they are additive with respect to the direct 3 In particular, the question about logarithmic partners of the energy-momentum tensor T (z) and other fields takes the form of a well-posed mathematical problem about the structure of projective W p+,p−modules. Logarithmic partners have been discussed, e.g., in [9,29,30,31,32] in the case c = 0, where the differential polynomial in T (z) whose logarithmic partner is sought coincides with T (z) itself.…”

Section: 4mentioning

confidence: 99%

Logarithmic extensions of minimal models: Characters and modular transformations

et al. 2006

View full text Add to dashboard Cite

ABSTRACT. We study logarithmic conformal field models that extend the (p, q) Virasoro minimal models. For coprime positive integers p and q, the model is defined as the kernel of the two minimal-model screening operators. We identify the field content, construct the W -algebra W p,q that is the model symmetry (the maximal local algebra in the kernel), describe its irreducible modules, and find their characters. We then derive the SL(2, Z)-representation on the space of torus amplitudes and study its properties. From the action of the screenings, we also identify the quantum group that is Kazhdan-Lusztig-dual to the logarithmic model. CONTENTS

show abstract

Section: 4mentioning

confidence: 99%

Logarithmic extensions of minimal models: Characters and modular transformations

et al. 2006

View full text Add to dashboard Cite

show abstract

“…Intertwined with this story is that of the c → 0 "catastrophe" [13,[19][20][21][22]. Here, one asks what happens to the operator product expansion of a primary field and its conjugate when c → 0.…”

Section: Introductionmentioning

confidence: 99%

On the percolation BCFT and the crossing probability of Watts

Ridout¹

2009

Nuclear Physics B

View full text Add to dashboard Cite

The logarithmic conformal field theory describing critical percolation is further explored using Watts' determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition changing operator which governs Watts' computation is identified with a primary field which does not fit naturally within the extended Kac table. Instead a "shifted" extended Kac table is shown to be relevant. Augmenting the previously known logarithmic theory based on Cardy's crossing probability by this field, a larger theory is obtained, in which new classes of indecomposable rank-2 modules are present. No rank-3 Jordan cells are yet observed. A highly non-trivial check of the identification of Watts' field is that no Gurarie-Ludwig-type inconsistencies are observed in this augmentation. The article concludes with an extended discussion of various topics related to extending these results including projectivity, boundary sectors and inconsistency loopholes. D RIDOUTHere, we wish to restrict ourselves to the conformal field theory description of critical percolation. Much of the interest in this conformal field theory stems from the simple realisation that it must be logarithmic (see [13] for an early statement to this effect). Indeed, it is almost universally agreed that critical percolation corresponds to a theory with vanishing central charge c (though [14] offers a dissenting opinion). A standard argument [15,16] then proves that any c = 0 conformal field theory built from irreducible Virasoro modules is trivial 1 . The alternative -that the theory is built from reducible but indecomposable Virasoro modules -leads to so-called logarithmic conformal field theory [17,18].Intertwined with this story is that of the c → 0 "catastrophe" [13,[19][20][21][22]. Here, one asks what happens to the operator product expansion of a primary field and its conjugate when c → 0. The standard form of this expansion shows that the coefficient of the energy-momentum tensor T (z) diverges unless the dimension of the primary field also tends to 0. Resolving this issue involves modifying the operator product expansion by adding "partner fields", and one quickly finds that this modification also leads to logarithmic conformal field theory. We mention that the derivation of the standard operator product expansion between a primary field and its conjugate breaks down at c = 0 [23] (because the energy-momentum tensor is null), so the "catastrophe" alluded to above is merely an expression of the subtlety involved in making sense of limits such as c → 0.Exactly the same problem occurs with the ∂ 2 T (z) and : T (z) T (z) : terms as c → −22 5 , unless the primary field dimension tends to 0 or −1 5 [23, 24]. The stage is now set for studying critical percolation via investigating c = 0 logarithmic conformal field theories. However, the number of such theories is probably infinite: Aside from the theories describing percolation and the other c = 0 statistical model, self-avoiding walks, there are theories con...

show abstract

“…The correlation functions involving the pseudo-operators then have the logarithmic terms [47]. There are various kinds of LCFT as classified in [48,49], but here we only discuss the type with vanishing central charge and nondegenerate vacuum. The usual way to study LCFT is just adding a nilpotent part to the conformal weight of the primary field [50,51].…”

Section: Basics Of Lcftmentioning

confidence: 99%

“…However, there is another approach to describe the LCFT when the central charge c = 0. It could be taken as the limit of an ordinary CFT with varying central charge c [48,49,[52][53][54][55][56]. In the following we will use the convention in [49].…”

Section: Basics Of Lcftmentioning

confidence: 99%

Holographic Rényi entropy in AdS3/LCFT2 correspondence

Chen

Song

Zhang

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

The recent study in AdS 3 /CFT 2 correspondence shows that the tree level contribution and 1-loop correction of holographic Rényi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the Rényi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of Rényi entanglement entropy in pure AdS 3 gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the Rényi entanglement entropy of two disjoint intervals with small cross ratio x, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order x 6 . To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS 3 gravity.

show abstract

Stress Energy tensor in LCFT and the Logarithmic Sugawara construction

Cited by 25 publications

References 51 publications

Logarithmic extensions of minimal models: Characters and modular transformations

Logarithmic extensions of minimal models: Characters and modular transformations

On the percolation BCFT and the crossing probability of Watts

Holographic Rényi entropy in AdS3/LCFT2 correspondence

Contact Info

Product

Resources

About