scholarly journals Perturbative renormalization of the $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed free massive Dirac fermion

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Anshuman Dey ◽  
Aryeh Fortinsky
Keyword(s):  
Field Theory ◽  
Two Dimensions ◽  
Second Order ◽  
Dirac Fermion ◽  
Coupling Constant ◽  
Reduction Formula ◽  
Classical Counterpart ◽  
Integrable Field Theory ◽  
Perturbative Renormalization ◽  
Integrable Field

Abstract In this paper we explicitly carry out the perturbative renormalization of the $$ T\overline{T} $$ T T ¯ -deformed free massive Dirac fermion in two dimensions up to second order in the coupling constant. This is done by computing the two-to-two S-matrix using the LSZ reduction formula and canceling out the divergences by introducing counterterms. We demonstrate that the renormalized Lagrangian is unambiguously determined by demanding that it gives the correct S-matrix of a $$ T\overline{T} $$ T T ¯ -deformed integrable field theory. Remarkably, the renormalized Lagrangian is qualitatively very different from its classical counterpart.

INTEGRABLE FIELD THEORY OF THE q-STATE POTTS MODEL WITH 0

1992 ◽  
Vol 07 (21) ◽  
pp. 5317-5335 ◽  
Author(s):  
LEUNG CHIM ◽  
ALEXANDER ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
Potts Model ◽  
Density Operator ◽  
Size Distributions ◽  
Quantum Field ◽  
Particle Content ◽  
Integrable Field Theory ◽  
Percolation Problem ◽  
S Matrix ◽  
Integrable Field

Two-dimensional quantum field theory obtained by perturbing the q-state Potts-model CFT (0<q<4) with the energy-density operator Φ(2, 1) is shown to be integrable. The particle content of this QFT is conjectured and the factorizable S matrix is proposed. The limit q→1 is related to the isotropic-percolation problem in 2D and so we make a few predictions about the size distributions of the percolating clusters in the scaling domain.

scholarly journals NONLINEAR SIGMA MODELS ON A HALF PLANE

1996 ◽  
Vol 11 (17) ◽  
pp. 3127-3143 ◽  
Author(s):  
M.F. MOURAD ◽  
R. SASAKI
Keyword(s):  
Sigma Models ◽  
Half Plane ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Two Dimensions ◽  
Field Theories ◽  
Integrable Field Theory ◽  
Infinite Set ◽  
Integrable Field ◽  
Nonlinear Sigma Models

In the context of integrable field theory with boundary, the integrable nonlinear sigma models in two dimensions, for example the O(N), the principal chiral, the CPN−1 and the complex Grassmannian sigma models, are discussed on a half plane. In contrast to the well-known cases of sine-Gordon, nonlinear Schrödinger and affine Toda field theories, these nonlinear sigma models in two dimensions are not classically integrable if restricted on a half plane. It is shown that the infinite set of nonlocal charges characterizing the integrability on the whole plane is not conserved for the free (Neumann) boundary condition. If we require that these nonlocal charges be conserved, then the solutions become trivial.

scholarly journals BOUND STATE BOUNDARY S MATRIX OF THE SINE-GORDON MODEL

1994 ◽  
Vol 09 (27) ◽  
pp. 4801-4810 ◽  
Author(s):  
SUBIR GHOSHAL
Keyword(s):  
Field Theory ◽  
Bound States ◽  
Bound State ◽  
Two Dimensional ◽  
Integrable Field Theory ◽  
S Matrix ◽  
State Boundary ◽  
Sine Gordon Model ◽  
Integrable Field

We study the boundary S matrix for the reflection of bound states of the two-dimensional sine-Gordon integrable field theory in the presence of a boundary.

scholarly journals THREE-LOOP CALCULATION OF THE ANYONIC FULL CLUSTER EXPANSION

1993 ◽  
Vol 08 (34) ◽  
pp. 3291-3299 ◽  
Author(s):  
R. EMPARAN ◽  
M.A. VALLE BASAGOITI
Keyword(s):  
Field Theory ◽  
Cluster Expansion ◽  
Cluster Coefficient ◽  
Second Order ◽  
Coupling Constant ◽  
Perturbative Correction ◽  
Chern Simons

We calculate the perturbative correction to every cluster coefficient of a gas of anyons through second order in the anyon coupling constant, as described by Chern-Simons field theory.

scholarly journals Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Alvise Bastianello ◽  
Benjamin Doyon ◽  
Gerard Watts ◽  
Takato Yoshimura
Keyword(s):  
Field Theory ◽  
Black Body ◽  
Black Body Radiation ◽  
Classical Field ◽  
Quasi Particle ◽  
Generalized Hydrodynamics ◽  
Integrable Field Theory ◽  
Classical Fields ◽  
Classical Integrable ◽  
Integrable Field

Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.

scholarly journals BOUNDARY S MATRIX AND BOUNDARY STATE IN TWO-DIMENSIONAL INTEGRABLE QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (21) ◽  
pp. 3841-3885 ◽  
Author(s):  
SUBIR GHOSHAL ◽  
ALEXANDER ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
Two Dimensional ◽  
Boundary State ◽  
Integrable Field Theory ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Boundary Analog ◽  
Sine Gordon Model ◽  
Integrable Quantum Field Theory ◽  
Integrable Field

We study integrals of motion and factorizable S matrices in two-dimensional integrable field theory with boundary. We propose the "boundary cross-unitarity equation," which is the boundary analog of the crossing-symmetry condition of the "bulk" S matrix. We derive the boundary S matrices for the Ising field theory with boundary magnetic field and for the boundary sine–Gordon model.

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