Composite operators in $$ T\overline{T} $$-deformed free QFTs

We study perturbative renormalization of the composite operators in the $$ T\overline{T} $$ T T ¯ -deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].

Nonperturbative aspects of the two-dimensional massive gauged Thirring model

In this paper, we present a study based on the use of functional techniques on the issue of insertions of massive fermionic fields in the two-dimensional massless gauged Thirring model. As it will be shown, the fermionic mass contributes to the Green's functions in a surprisingly simple way, leaving therefore the original nonperturbative nature of the massless results still intact in the massive theory. Also, by means of complementarity, we present a second discussion of the massive model, now at its bosonic representation.

Massive Conformal Gravity

We construct a massive theory of gravity that is invariant under conformal transformations. The massive action of the theory depends on the metric tensor and a scalar field, which are considered the only field variables. We find the vacuum field equations of the theory and analyze its weak-field approximation and Newtonian limit.

ON UNITARITY OF A LINEARIZED YANG–MILLS FORMULATION FOR MASSLESS AND MASSIVE GRAVITY WITH PROPAGATING TORSION

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang–Mills formulation for gravity in a (2+1)-dimensional space–time. In the massless case, we show that the theory contains three degrees of freedom and only one is a nonunitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert–Einstein–Fierz–Pauli unitary massive theory plus three massless modes, two of them represents nonunitary ones. Finally, we confirm the existence of a family of unitary Yang–Mills-extended theories which are classically consistent with Einstein's solutions coming from nonmassive and topologically massive gravity. The unitarity of these Yang–Mills-extended theories is shown in a perturbative regime. A possible way to perform a nonperturbative study is remarked.

BFT Hamiltonian Embedding of Massive Theory with One- and Two-Form Gauge Fields

Without resorting to the symplectic condition, we rigorously study the constraint structure of the topologically massive theory with one- and two-form fields in the framework of Batalin–Fradkin–Tyutin Hamiltonian embedding procedure. Through this full analysis we obtain a new type of Wess–Jumino action with novel symmetry, which is originated from the topological coupling term, as well as the Stückelberg action related to the explicit gauge breaking mass terms from the original theory.

NON-EXISTENCE OF LOCAL INTEGRALS OF MOTION IN THE MULTI-DEFORMED ISING MODEL

We confirm the non-integrability of the multi-deformed Ising model — an already expected result. After deforming with the energy operator ϕ1,3, we use the Majorana free fermionic representation for the massive theory to show that, besides the trivial one, no local integrals of motion can be built in the theory arising from perturbing with both energy and spin operators.

Nonsymmetric Gravitational Theories in Hamiltonian Form

The dynamics of a class of nonsymmetric gravitational theories are presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as the canonical coordinates and the densitized components of the inverse of the fundamental tensor as conjugate momenta. The phase space of the symmetric sector is enlarged over that of conventional treatments of general relativity by a canonical pair that represents the metric density and its conjugate, removable by imposing strongly an associated pair of second-class constraints and introducing Dirac brackets. In the antisymmetric sector, all six components of the fundamental tensor contribute conjugate pairs for the massive theory, and the absence of additional constraints gives six configuration space degrees of freedom per space–time point.