Exact Correlation Functions in the Brownian Loop Soup

We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system known as the Brownian Loop Soup. These correlation functions depend on multiple continuous parameters: the insertion points of the operators, the intensity of the soup, and the charges of the operators. In the case of the four-point function there is non-trivial dependence on five continuous parameters: the cross-ratio, the intensity, and three real charges. The four-point function is crossing symmetric. We analyze its conformal block expansion and discover a previously unknown set of new conformal primary operators.Comment: 28 pages, 2 figures; Eq. (20) correcte

Gravitational wave echoes from black hole area quantization

Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of black holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Bekenstein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detectors. In particular, we find distorted gravitational-wave “echoes” in the post-merger waveform describing the inspiral and merger of two black holes. These echoes have a specific frequency content that is characteristic of black hole horizon area quantization.Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of black holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Bekenstein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detectors. In particular, we find distorted gravitational-wave "echoes" in the post-merger waveform describing the inspiral and merger of two black holes. These echoes have a specific frequency content that is characteristic of black hole horizon area quantization

The Brownian loop soup stress-energy tensor

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

Scalar Conformal Primary Fields in the Brownian Loop Soup

The Brownian loop soup is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity λ> 0 , with central charge c= 2 λ. Recent progress resulted in an analytic form for the four-point function of a class of scalar conformal primary “layering vertex operators” Oβ with dimensions (Δ , Δ) , with Δ=λ10(1-cosβ), that compute certain statistical properties of the model. The Virasoro conformal block expansion of the four-point function revealed the existence of a new set of operators with dimensions (Δ + k/ 3 , Δ + k′/ 3) , for all non-negative integers k, k′ satisfying |k-k′|=0mod3. In this paper we introduce the edge counting field E(z) that counts the number of loop boundaries that pass close to the point z. We rigorously prove that the n-point functions of E are well defined and behave as expected for a conformal primary field with dimensions (1/3, 1/3). We analytically compute the four-point function 〈 Oβ(z1) O-β(z2) E(z3) E(z4) 〉 and analyze its conformal block expansion. The operator product expansions of E× E and E× Oβ contain higher-order edge operators with “charge” β and dimensions (Δ + k/ 3 , Δ + k/ 3). Hence, we have explicitly identified all scalar primary operators among the new set mentioned above. We also re-compute the central charge by an independent method based on the operator product expansion and find agreement with previous methods

TT¯ TT‾ T\overline{T} type deformation in the presence of a boundary

Abstract We continue the study of a recently proposed solvable irrelevant deformation of an AdS3/CFT2 correspondence that leads in the UV to a theory with Hagedorn spectrum. This can be thought of as a single trace analog of the TT¯ $$T\overline{T}$$ -deformation of the dual CFT2. Here we focus on the deformed worldsheet theory in presence of a conformal boundary. First, we compute the expectation value of a bulk primary operator on the disc geometry. We give a closed expression for such observable, from which we obtain the anomalous conformal dimension induced by the deformation. We compare the result with that coming from the computation of the 2-point correlation function on the sphere, finding exact agreement. We perform the computation using different techniques and making a comparative analysis of different regularization schemes to solve the logarithmically divergent integrals. This enables us to perform further consistency checks of our result by computing other observables of the deformed theory: we compute both the bulk-boundary 2-point and the boundary-boundary 2-point functions and are able to reproduce the anomalous dimensions of both boundary and bulk operators