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].

Superspace formulation of massive half-integer superspin

An explicit form for the Lagrangian of a massive arbitrary half-integer super-spin Y = s + 1/2 supermultiplet is obtained in 4D,$$ \mathcal{N} $$ N = 1 superspace. This is accomplished by the introduction of a tower of pairs of auxiliary superfields of increasing rank which are required to vanish on-shell for free theories. In the massless limit almost all auxiliary super- fields decouple except one, which plays the role of compensator as required by the emergent gauge redundancy of the Lagrangian description of the massless theory. The number of off-shell degrees of freedom carried by the theory is $$ \frac{8}{3} $$ 8 3 (s + 1)(4s2 + 11s + 3). For s = 1 our results are in agreement with those obtained in [1].

Partially massless theory in three dimensions and self-dual massive gravity

Partially massless theory in three dimensions is revisited and its relationship with the self-dual massive gravity is considered. The only mode of the partially massless theory is shown explicitly through an action for a scalar field on (A)dS background. This fact can be generalized to higher dimensions. This degree of freedom is altered when a triadic Chern–Simons is introduced, giving rise to the self-dual massive gravity on (A)dS background. We present another physical system with partially massless symmetry and its connection with topologically massive gravity is discussed.

Renormalization group approach for Lorentz-violating scalar field theory at all loop orders

We compute, both explicitly, at least, up to next-to-leading order and in a proof by induction for all loop levels, the critical exponents for thermal Lorentz-violating O([Formula: see text]) self-interacting scalar field theory. They are evaluated in a massless theory renormalized at arbitrary external momenta, where a reduced number of Feynman diagrams is needed. The results are presented and shown to be identical to that found previously in distinct theories renormalized at different renormalization schemes. Finally, we give both mathematical explanation and physical interpretation for them based on coordinates redefinition techniques and symmetry ideas, respectively.

Geometry of mass

We study the effect of mass on geometric descriptions of gauge field theories. In an approach in which the massless theory resembles general relativity, the introduction of the mass entails non-zero torsion and the generalization to Einstein–Cartan–Sciama–Kibble theories. The relationships to pure torsion formulations (teleparallel gravity) and to higher gauge theories are also discussed.

The Condensate for SU(2) Gauge Theory in 1 + 1 Dimensions Coupled to Massless Adjoint Fermions

We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint represention the gauge group is actually SU(2)/Z2, which possesses nontrivial topology. In particular, there are two distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this feature is realized in light-front quantization, using discretization of x- as an infrared regulator. We find exact expressions for the vacuum states and construct the analog of the θ vacuum. We calculate the bilinear condensate of the model. We argue that this condensate does not effect the spectrum of the massless theory but gives the string tenson of the massive theory.

ON THE VANISHING COUPLINGS IN $\hat{A}\hat{D}\hat{E}$ AFFINE TODA FIELD THEORIES

We show that certain vanishing couplings in the [Formula: see text] affine Toda field theories remain vanishing even after higher-order corrections are included. This is a requisite property for the Lagrangian formulation of the theory. We develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. We show that the nonrenormalization comes from the Dynkin automorphism of the Lie algebra associated with these theories. A charge balance condition plays an important role in our scheme. The all-order nonrenormalization of vanishing couplings in [Formula: see text] affine Toda field theory is also proved in a standard massive scheme.