A
bstract
We study unitary minimal models coupled to Liouville gravity using Douglas string equation. Our approach is based on the assumption that there exist an appropriate solution of the Douglas ...string equation and some special choice of the resonance transformation such that necessary selection rules of the minimal Liouville gravity are satisfied. We use the connection with the Frobenius manifold structure. We argue that the flat coordinates on the Frobenius manifold are the most appropriate choice for calculating correlation functions. We find the appropriate solution of the Douglas string equation and show that it has simple form in the flat coordinates. Important information is encoded in the structure constants of the Frobenius algebra. We derive these structure constants in the canonical coordinates and in the physically relevant domain in the flat coordinates. We find the leading terms of the resonance transformation and express the coefficients of the resonance transformation in terms of Jacobi polynomials.
A
bstract
We present a method for the first principles calculation of tachyon one-point amplitudes in (2
,
2
p
+ 1) minimal Liouville gravity defined on a torus. The method is based on the higher ...equations of motion in the Liouville CFT. These equations were earlier successfully applied for analytic calculations of the amplitudes in the spherical topology. We show that this approach allows to reduce the moduli integrals entering the definition of the torus amplitudes to certain boundary contributions, which can be calculated explicitly. The results agree with the calculations performed in the matrix models approach.
A
bstract
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the
A
q
integrable hierarchy ...via the resonance transformations, which are in turn fixed by conformal selection rules. One of the main problems in this approach is to choose the solution of the Douglas string equation that is relevant for MLG. The appropriate solution was recently found using connection with the Frobenius manifolds. We use this solution to investigate three- and four-point correlators in the unitary MLG models. We find an agreement with the results of the original approach in the region of the parameters where both methods are applicable. In addition, we find that only part of the selection rules can be satisfied using the resonance transformations. The physical meaning of the nonzero correlators, which before coupling to Liouville gravity are forbidden by the selection rules, and also the modification of the dual formulation that takes this effect into account remains to be found.
A
bstract
We propose the holographic interpretation of the 1-point conformal block on a torus in the semiclassical regime. To this end we consider the linearized version of the block and find its ...coefficients by means of the perturbation procedure around natural seed configuration corresponding to the zero-point block. From the AdS/CFT perspective the linearized block is given by the geodesic length of the tadpole graph embedded into the thermal AdS plus the holomorphic part of the thermal AdS action.
A recently proposed correspondence between 4-dimensional
SUSY SU(
k
) gauge theories on
and SU(
k
) Toda-like theories with
Z
m
parafermionic symmetry is used to construct four-point
super Liouville ...conformal block, which corresponds to the particular case
k
=
m
= 2.
The construction is based on the conjectural relation between moduli spaces of SU(2) instantons on
and algebras like
. This conjecture is confirmed by checking the coincidence of number of fixed points on such instanton moduli space with given instanton number
N
and dimension of subspace degree
N
in the representation of such algebra.
We evaluate one-point correlation numbers on the torus in the Liouville theory coupled to the conformal matter M(2,2p+1). We find agreement with the recent results obtained in the matrix model ...approach.
In this work, we propose an approach for electromagnetic shower generation on a track level. Currently, Monte Carlo simulation occupies 50-70% of total computing resources that are used by physicists ...experiments worldwide. Thus, speedup of the simulation step allows to reduce simulation cost and accelerate synthetic experiments. In this paper, we suggest dividing the problem of shower generation into two separate issues: graph generation and tracks features generation. Both these problems can be efficiently solved with a cascade of deep autoregressive generative network and graph convolution network. The novelty of the proposed approach lies in the application of graph neural networks to the generation of a complex recursive physical process.
Traces of electromagnetic showers in the neutrino experiments may be considered as signals of dark matter particles. For example, SHiP experiment is going to use emulsion film detectors similar to ...the ones designed for OPERA experiment from dark matter search. The goal of this research is to develop an algorithm that can identify traces of electromagnetic showers in particle detectors, so it would be possible to analyse and compare various dark matter hypothesis. Both real data and signal simulation samples for this research come from OPERA experiment. Also we have used exploited algorithm for electromagnetic showers identification as a baseline. Although in this research we have used no hints about shower origin.
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