Searcharxiv⌕ Search

arXiv subjects

F. Smirnov

Publications and source records attributed to F. Smirnov.

At least 19 recordsLinked to original sources
arXiv2019

Nonconservative traceless type gravity

Extensions of the gravity theory in order to obtain traceless field equations have been widely considered in the literature. The leading example of such class of theories is the unimodular gravity, but there are other possibilities like the mimetic gravity and the Rastall gravity with a coupling parameter $λ= 1/2$. The unimodular gravity proposal is a very interesting approach in other to address the cosmological constant problem. When coupled to matter such theories may imply that the energy-momentum tensor is not divergence free anymore. In this paper, a unimodular type theory will be developed by evading the conservation $T^{μν}_{\, ; μ}=0$. The cosmological consequences of the later, both at background as well as for scalar and tensor perturbations, are explored. Possible further extensions of this approach are discussed as well as its connection with the traditional unimodular gravity.

gr-qc↗
arXiv2019

One point functions of fermionic operators in the Super Sine Gordon model

We describe the integrable structure of the space of local operators for the supersymmetric sine-Gordon model. Namely, we conjecture that this space is created by acting on the primary fields by fermions and a Kac-Moody current. We proceed with the computation of the one-point functions. In the UV limit they are shown to agree with the alternative results obtained by solving the reflection relations.

hep-th↗
arXiv2019

Fermion-current basis and correlation functions for the integrable spin 1 chain

We use the fermion-current basis in the space of local operators for the computation of the expectation values for the integrable spin chain of spins 1. Our main tool consists in expressing a given local operators in the fermion-current basis. For this we use the same method as in the spin 1/2 case which is based on the arbitrariness of the Matsubara data.

math-ph↗
arXiv2018

New exact results on density matrix for XXX spin chain

Using the fermionic basis we obtain the expectation values of all $\slt$-invariant and $C$-invariant local operators on 10 sites for the anisotropic six-vertex model on a cylinder with generic Matsubara data. This is equivalent to the generalised Gibbs ensemble for the XXX spin chain. In the case when the $\slt$ and $C$ symmetries are not broken this computation is equivalent to finding the entire density matrix up to 10 sites. As application, we compute the entanglement entropy without and with temperature, and compare the results with CFT predictions.

math-ph↗
arXiv2017

Suzuki equations and integrals of motion for supersymmetric CFT

Using equations proposed by J. Suzuki we compute numerically the first three integrals of motion for $N=1$ supersymmetric CFT. Our computation agrees with the results of ODE-CFT correspondence which was explained in a more general context by S. Lukyanov.

hep-th↗
arXiv2016

New results on integrable structure of conformal field theory

We explain how to incorporate the action of local integrals of motion into the fermionic basis for the sine-Gordon model and its UV CFT. The examples up to the level 4 are presented. Numerical computation support the results. Possible applications are discussed.

hep-th↗
arXiv2015

Problems with using separated variables for computing expectation values for higher ranks

We consider the simplest classical integrable model corresponding to a non-hyperelliptic spectral curve. We show that a certain complicated integral occurs when computing the average of observables in this model. This integral does not factorise. Since similar problems should also exist in the quantum case, we think that a serious question arises of how to deal with these integrals.

math-ph↗
arXiv2014

Creation operators for the Fateev-Zamolodchikov spin chain

In our previous works on the XXZ chain of spin one half, we have studied the problem of constructing a basis of local operators whose members have simple vacuum expectation values. For this purpose a pair of fermionic creation operators have been introduced. In this article we extend this construction to the spin one case. We formulate the fusion procedure for the creation operators, and find a triplet of bosonic as well as two pairs of fermionic creation operators. We show that the resulting basis of local operators satisfies the dual reduced qKZ equation.

hep-th↗
arXiv2013

Reflection relations and fermionic basis

There are two approaches to computing the one-point functions for sine-Gordon model in infinite volume. One is a bootstrap type procedure based on the reflection relations. Another uses the fermionic basis which was originally found for the lattice six-vertex model. In this paper we show that the two approaches are deeply interrelated.

hep-th↗
arXiv2013

Hidden Grassmann structure in the XXZ model V: sine-Gordon model

We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on the plane. In the present paper we make an essential addition by giving a connection between various primary fields in terms of yet another kind of fermions. The one-point functions of primary fields and descendants are expressed in terms of a single function defined via the data from the thermodynamic Bethe Ansatz equations.

hep-th↗
arXiv2010

Hidden Grassmann Structure in the XXZ Model IV: CFT limit

The Grassmann structure of the critical XXZ spin chain is studied in the limit to conformal field theory. A new description of Virasoro Verma modules is proposed in terms of Zamolodchikov's integrals of motion and two families of fermionic creation operators. The exact relation to the usual Virasoro description is found up to level 6.

hep-th↗
arXiv2008

Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction

We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in the infinite volume limit while keeping the Matsubara (or Trotter) direction finite. The result is expressed in terms of two basic quantities: a ratio $ρ(\z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator $ω(\z,ξ)$. We explain that the latter is interpreted as the canonical second kind differential in the theory of deformed Abelian integrals.

math-ph↗
arXiv2008

Hidden Grassmann Structure in the XXZ Model II: Creation Operators

In this article we unveil a new structure in the space of operators of the XXZ chain. We consider the space of all quasi-local operators, which are products of the disorder field with arbitrary local operators. In analogy with CFT the disorder operator itself is considered as primary field. In our previous paper, we have introduced the annhilation operators which mutually anti-commute and kill the primary field. Here we construct the creation counterpart and prove the canonical anti-commutation relations with the annihilation operators. We show that the ground state averages of quasi-local operators created by the creation operators from the primary field are given by determinants.

hep-th↗
arXiv2007

Fermionic basis for space of operators in the XXZ model

In the recent study of correlation functions for the infinite XXZ spin chain, a new pair of anti-commuting operators $b(z), c(z)$ was introduced. They act on the space of quasi-local operators, which are local operators multiplied by the disorder operator. For the inhomogeneous chain with the spectral parameters $ξ_{k}$, these operators have simple poles at $z^2=ξ_{k}^2$. The residues are denoted by $b_{k}, c_{k}$. At $q=i$, we show that the operators $b_{k}, c_{k}$ are cubic monomials in free fermions. In other words, the action of these operators is very simple in the fermion basis. We give an explicit construction of these fermions. Then, we show that the existence of the fermionic basis is a consequence of the Grassmann relation, the equivariance with respect to the action of the symmetric group and the reduction property, which are all valid for the operators $b_{k}, c_{k}$ in the case of generic $q$.

hep-th↗