We systematically construct derivative self-interactions for massless and massive 2-forms. There exists a no-go theorem in the literature for constructing Galileon-like Lagrangians in four dimensions for the 2-form with gauge invariance, the Kalb-Rammond field. The presence of non-minimal couplings strongly relies on the contraction with divergenceless tensors. In four dimensions these are the Einstein tensor and the double dual Riemann tensor. Even though they are divergenceless on their own, their combination ceases to be. In the case of massless 2-forms we are not able to establish non-minimal couplings of the 2-form to the gravity sector with second order equations of motion due to the impossibility of building consistent combinations of divergenceless tensors. Using the systematical construction in terms of the Levi-Civita tensor, we aim at constructing Galileon-like derivative self-interactions for the massive 2-form. Apart from $L_2$ and $L_4$ we are not able to construct further Galileon-like Lagrangians. For the massive case, an important non-minimal coupling between the 2-form and the double dual Riemann tensor arises, which receives additional support from the decoupling limit. Promoting the interactions in $L_4$ requires the presence of appropriate non-minimal couplings and we give concrete examples for this.
We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky model. Using an iterative approach and eliminating the mediating field by means of the covariant Green function we arrive at a Lagrangian density containing many-point time-nonlocal interaction terms. In low-order approximations of $ϕ^3{+}ϕ^4$ theory we obtain the usual two-current interaction as well as a three-current interaction of a confining type. The same result is obtained without approximation for a version of the dipole model. The transition to the Hamiltonian formalism and subsequent canonical quantization is …
We consider the Lagrangian of a vector field with derivative self-interactions with a priori arbitrary coefficients. Starting with a flat space-time we show that for a special choice of the coefficients of the self-interactions the ghost-like pathologies disappear. For this we use the degeneracy condition of the Hessian. This constitutes the Galileon-type generalization of the Proca action with only three propagating physical degrees of freedom. The longitudinal mode of the vector field is associated to the usual Galileon interactions for a specific choice of the overall functions. In differen…
Mass dimension one quantum fields, constructed upon eigenspinors of the charge conjugation operator with dual helicity (ELKO), are prime candidates to describe dark matter. Their interaction with the photon and the proton, in scattering processes, are here explored and discussed, using both the standard QFT with a Maxwell gauge field and a generalized QFT also involving a Podolsky gauge sector. Renormalization and radiative corrections are analyzed in the ELKO setup, in the context of a generalized spinor dual and the twisted conjugation, both yielding unitarity. Several applications are scrut…
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and trigonometric functions are defined.
A class of 1+1 dimensional supersymmetric theories with four-fermionic interaction will be built from scratch. The vacua of selected examples will be examined in the 't Hooft limit and compared to the Gross-Neveu model.
We consider perturbative quantum field theory in the causal framework. Gauge invariance is, in this framework, an identity involving chronological products of the interaction Lagrangian; it express the fact that the scattering matrix must leave invariant the sub-space of physical states. We are interested in generalizations of such identity involving Wick sub-monomials of the interaction Lagrangian. The analysis can be performed by direct computation in the lower orders of perturbation theory; guided by these computations we conjecture a generalization for arbitrary orders.
We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients, and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghost-like pathologies in these interactions disappear for special choices of the polynomial interactions, and argue that this result remains true to all orders in the decoupling limit. Moreover,…
We study the critical properties of scalar field theories in $d+1$ dimensions with $O(N)$ invariant interactions localized on a $d$-dimensional boundary. By a combination of large $N$ and epsilon expansions, we provide evidence for the existence of non-trivial $O(N)$ BCFTs in $1<d<4$. Due to having free fields in the bulk, these models possess bulk higher-spin currents which are conserved up to terms localized on the boundary. We suggest that this should lead to a set of protected spinning operators on the boundary, and give evidence that their anomalous dimensions vanish. We also discuss the …
Colored tensor models generalize matrix models in higher dimensions. They admit a 1/N expansion dominated by spherical topologies and exhibit a critical behavior strongly reminiscent of matrix models. In this paper we generalize the colored tensor models to colored models with generic interaction, derive the Schwinger Dyson equations in the large N limit and analyze the associated algebra of constraints satisfied at leading order by the partition function. We show that the constraints form a Lie algebra (indexed by trees) yielding a generalization of the Virasoro algebra in arbitrary dimension…
We review different constructions of Galileon theories in both flat and curved space, and for both single scalar field models as well as multi-field models. Our main emphasis is on the formal mathematical properties of these theories and their construction.
The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, the are no TM discrete modes t…
We describe a method of writing down the exact interacting gauge invariant equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a ``band'' of finite width. As in the free case, the fields appear to be massless in one higher dimension. Although a proof of the consistency and gauge invariance to all or…
The generalization of the Gross-Neveu model for noncommutative 3+1 space-time has been analyzed. We find indications that the chiral symmetry breaking occurs for an inhomogeneous background as in the LOFF phase in condensed matter.
A detailed analysis of convergence properties of the Andreozzi-Lee-Suzuki iteration method, which is used for the calculation of low-momentum effective potentials Vlowk is presented. After summarizing different modifications of the iteration method for one-flavor channel we introduce a simple model in order to study the generalization of the iteration method to multi-flavor channels. The failure of a straightforward generalization is discussed. The introduction of a channel-dependent cutoff cures the conceptual and technical problems. This novel method has already been applied successfully for…
We describe a method of writing down interacting equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a ``band'' of finite width. The interaction equations expressed in terms of loop variables, has a simple invariance that is exact even off shell. A consistent definition of space-time fields requires…
We study matrix models involving Pfaffian interactions as generalizations of the standard $β= 1$ and $β= 4$ matrix models. We present the Pfaffian formulas for the partition function and the characteristic polynomial averages. We also explore the matrix chain with the Pfaffian interaction, which realizes the BCD-type quiver matrix models.
The SYK model: fermions with a $q$-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large $N$ models. We generalize SYK to include $f$ flavors of fermions, each occupying $N_a$ sites and appearing with a $q_a$ order in the interaction. Like SYK, this entire class of models generically has an infrared fixed point. We compute the infrared dimensions of the fermions, and the spectrum of singlet bilinear operators. We show that there is always a dimension-two operator in the spectrum, which implies that, like in SYK, there is breaking of conformal …
Tensor models are natural generalizations of matrix models. The interactions and observables in the case of unitary invariant models are generalizations of matrix traces. Some notable interactions in the literature include the melonic ones, the tetrahedral one as well as the planar ones in rank three, or necklaces in even ranks. Here we introduce generalized melonic interactions which generalize the melonic and necklace interactions. We characterize them as tree-like gluings of quartic interactions. We also completely characterize the Feynman graphs which contribute to the large $N$ limit. For…
We construct integrable generalizations of the elliptic Calogero-Sutherland-Moser model of particles with spin, involving noncommutative spin interactions. The spin coupling potential is a modular function and, generically, breaks the global spin symmetry of the model down to a product of U(1) phase symmetries. Previously known models are recovered as special cases.
