String theory in polar coordinates and the vanishing of the one-loop Rindler entropy

Mertens, Thomas G.; Verschelde, Henri; Захаров, В. И.

doi:10.1007/jhep08(2016)113

Cited by 8 publications

(12 citation statements)

References 116 publications

(389 reference statements)

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“…To understand the limitations of such a procedure, a concrete avenue would be to further investigate strings on the SL(2, R)/U (1) cigar background, which has Rindler space as a parametric limit (see e.g. [37,[66][67][68][69][70][71][72][73][74]).…”

Section: Resultsmentioning

confidence: 99%

“…a trace over a yet-to-be-determined Hilbert space). In recent years, many of these Euclidean calculations have been performed, both in QFT as in string theory [28][29][30][31][32][33][34][35][36][37]. For Maxwell theory, Kabat found a contribution to the partition function due to a coupling of non-scalar fields to the conical singularity introduced in the Euclidean calculation: the contact term.…”

Section: Introductionmentioning

confidence: 99%

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Edge state quantization: vector fields in Rindler

Blommaert

Mertens

Verschelde

et al. 2018

J. High Energ. Phys.

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We present a detailed discussion of the entanglement structure of vector fields through canonical quantization. We quantize Maxwell theory in Rindler space in Lorenz gauge, discuss the Hilbert space structure and analyze the Unruh effect. As a warm-up, in 1+1 dimensions, we compute the spectrum and prove that the theory is thermodynamically trivial. In d + 1 dimensions, we identify the edge sector as eigenstates of horizon electric flux or equivalently as states representing large gauge transformations, localized on the horizon. The edge Hilbert space is generated by inserting a generic combination of Wilson line punctures in the edge vacuum, and the edge states are identified as Maxwell microstates of the black hole. This construction is repeated for Proca theory. Extensions to tensor field theories, and the link with Chern-Simons are discussed.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Edge state quantization: vector fields in Rindler

Blommaert

Mertens

Verschelde

et al. 2018

J. High Energ. Phys.

Self Cite

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“…It would in any case be interesting to understand better the role of edge states within string theory and its relation to the old Susskind-Uglum picture of horizon-piercing strings (see e.g. [62] for a 2d example, and [63][64][65][66] for a variety of results in this direction using Euclidean techniques).…”

Section: Discussionmentioning

confidence: 99%

Edge dynamics from the path integral — Maxwell and Yang-Mills

Blommaert

Mertens

Verschelde

2018

J. High Energ. Phys.

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114

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We derive an action describing edge dynamics on interfaces for gauge theories (Maxwell and Yang-Mills) using the path integral. The canonical structure of the edge theory is deduced and the thermal partition function calculated. We test the edge action in several applications. For Maxwell in Rindler space, we recover earlier results, now embedded in a dynamical canonical framework. A second application is 2d Yang-Mills theory where the edge action becomes just the particle-on-a-group action. Correlators of boundary-anchored Wilson lines in 2d Yang-Mills are matched with, and identified as correlators of bilocal operators in the particle-on-a-group edge model. Recently in [26], using canonical quantization of the Maxwell action, we presented an alternative procedure that gives rise to a canonical structure on the boundary of Maxwell: instead of saving large gauge-invariance by introducing a new variable, we abandon it completely and promote the large gauge degrees of freedom φ themselves to physical variables, conjugate to the boundary charges E(x). This promotion of large gauge parameters to physical boundary variables is a key ingredient in topological theories such as 3d Chern-Simons, where they make up the boundary theory dual to the entire bulk theory.The question arises whether there is a boundary action that gives rise to this canonical structure. 1 Given such an action, it would be possible to study boundary correlation functions and real-time dynamics. In this work, we derive this boundary edge action for Maxwell and Yang-Mills theory. The result is a Lorentzian action that depends on the boundary gauge field g and the boundary current density J :where A[J ] denotes the on-shell evaluation of the gauge field sourced by the boundary current J .1 A similar goal is being pursued by Geiller and Jai-akson (private communication). 5)2 Note that J α is a contravariant tensor density of weight +1, as with our definition it already includes the metric pullback √ −h factor on ∂M. We use this definition to match more naturally with the canonical formalism in curved space, where conjugate momenta are tensor densities. 3 We will show further on that ∂nφ does not figure in the action, and hence only the variables φ| ∂M and ∂αφ| ∂M appear.

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“…The quantum dimension is the measure of the effective degrees of freedom of a local operator and it is a kind of topological quantity. In various dimensional CFTs, REE has been studied in [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35] from various perspectives.…”

Section: Introductionmentioning

confidence: 99%

“…The papers [16] [17] [19] [20] mainly concentrated on entanglement entropy in higherdimensional field theory. The authors of [18] have found the REE of local excited states in large central charge 1 + 1 dimensional CFTs from holography.…”

Section: Introductionmentioning

confidence: 99%

Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs

2019

Phys. Rev. D

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The Rényi entanglement entropy (REE) of the states excited by local operators in two-dimensional irrational conformal field theories (CFTs), especially in Liouville field theory (LFT) and N = 1 super-Liouville field theory (SLFT), has been investigated. In particular, the excited states obtained by acting on the vacuum with primary operators were considered. We start from evaluating the second REE in a compact c = 1 free boson field theory at generic radius, which is an irrational CFT. Then we focus on the two special irrational CFTs, e.g., LFT and SLFT. In these theories, the second REE of such local excited states becomes divergent in early and late time limits. For simplicity, we study the memory effect of REE for the two classes of the local excited states in LFT and SLFT. In order to restore the quasiparticles picture, we define the difference of REE between target and reference states, which belong to the same class. The variation of the difference of REE between early and late time limits always coincides with the log of the ratio of the fusion matrix elements between target and reference states. Furthermore, the locally excited states by acting generic descendent operators on the vacuum have been also investigated. The variation of the difference of REE is the summation of the log of the ratio of the fusion matrix elements between the target and reference states, and an additional normalization factor. Since the identity operator (or vacuum state) does not live in the Hilbert space of LFT and SLFT and no discrete terms contribute to REE in the intermediate channel, the variation of the difference of REE between target and reference states is no longer the log of the quantum dimension which is shown in the 1+1-dimensional rational CFTs (RCFTs). *

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String theory in polar coordinates and the vanishing of the one-loop Rindler entropy

Cited by 8 publications

References 116 publications

Edge state quantization: vector fields in Rindler

Edge state quantization: vector fields in Rindler

Edge dynamics from the path integral — Maxwell and Yang-Mills

Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs

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