Exact correlation functions in the Brownian Loop Soup

Camia, Federico; Foit, Valentino F.; Gandolfi, Alberto; Kleban, Matthew

doi:10.1007/jhep07(2020)067

Cited by 5 publications

(30 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The term containing T (z) appears at order ).) This can be deduced from the analysis carried out in [4], as shown in Figure 1a. Thus one can identify…”

Section: Identificationmentioning

confidence: 91%

“…This limiting field is further studied in [4], where its canonically normalized version is denoted by O β . 4 For a domain D with a boundary ∂D and a point ζ ∈ ∂D, the boundary field B δ ε (ζ) studied in this paper counts the number of loops with diameter at least δ passing within a short-distance ε of ζ. This is a boundary version of the edge field studied in [5] and discussed in Section 1.2 below.…”

Section: Preliminary Definitionsmentioning

confidence: 99%

“…are determined by the Virasoro algebra and are given by 2∆(β)/c and 1/2, respectively [12]; the central charge 6 as explained in [4], which gives…”

Section: Correlation Functionsmentioning

confidence: 99%

“…It provides an interesting and useful link between Brownian motion, field theory, and statistical mechanics. Inspired and partly motivated by these connections, in [3][4][5] we introduced and studied operators that compute properties of the BLS, discovering new families of conformal primary fields and analyzing the operator content of the emerging conformal field theory.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Brownian loop soup stress-energy tensor

Camia¹,

Foit²,

Gandolfi³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The Brownian loop soup (BLS) is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity λ > 0. Recently, we constructed families of operators in the BLS and showed that they transform as conformal primary operators. In this paper we provide an explicit expression for the BLS stress-energy tensor and compute its operator product expansion with other operators. Our results are consistent with the conformal Ward identities and our previous result that the central charge is c = 2λ. In the case of domains with boundary we identify a boundary operator that has properties consistent with the boundary stress-energy tensor. We show that this operator generates local deformations of the boundary and that it is related to a boundary operator that induces a Brownian excursion starting or ending at its insertion point.

show abstract

“…The term containing T (z) appears at order ).) This can be deduced from the analysis carried out in [4], as shown in Figure 1a. Thus one can identify…”

Section: Identificationmentioning

confidence: 91%

Section: Preliminary Definitionsmentioning

confidence: 99%

“…are determined by the Virasoro algebra and are given by 2∆(β)/c and 1/2, respectively [12]; the central charge 6 as explained in [4], which gives…”

Section: Correlation Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Brownian loop soup stress-energy tensor

Camia¹,

Foit²,

Gandolfi³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Both the layering and the winding field present interesting and unusual features, such as a periodic spectrum of conformal dimensions. An explicit expression for the four-point function of the layering model was recently obtained in [13].…”

mentioning

confidence: 99%

Brownian Loops, Layering Fields and Imaginary Gaussian Multiplicative Chaos

Camia¹,

Gandolfi²,

Peccati

et al. 2021

Commun. Math. Phys.

Self Cite

View full text Add to dashboard Cite

We study fields reminiscent of vertex operators built from the Brownian loop soup in the limit as the loop soup intensity tends to infinity. More precisely, following Camia et al. (Nucl Phys B 902:483–507, 2016), we take a (massless or massive) Brownian loop soup in a planar domain and assign a random sign to each loop. We then consider random fields defined by taking, at every point of the domain, the exponential of a purely imaginary constant times the sum of the signs associated to the loops that wind around that point. For domains conformally equivalent to a disk, the sum diverges logarithmically due to the small loops, but we show that a suitable renormalization procedure allows to define the fields in an appropriate Sobolev space. Subsequently, we let the intensity of the loop soup tend to infinity and prove that these vertex-like fields tend to a conformally covariant random field which can be expressed as an explicit functional of the imaginary Gaussian multiplicative chaos with covariance kernel given by the Brownian loop measure. Besides using properties of the Brownian loop soup and the Brownian loop measure, a main tool in our analysis is an explicit Wiener–Itô chaos expansion of linear functionals of vertex-like fields. Our methods apply to other variants of the model in which, for example, Brownian loops are replaced by disks.

show abstract