Related papers: Randomly Branched Polymers and Conformal Invarianc…
The free Maxwell theory in D<>4 dimensions provides a physical example of a unitary, scale invariant theory which is NOT conformally invariant. The easiest way to see this is that the field strength operator F_mn is neither a primary nor a…
In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot…
We construct 7-dimensional quantum field theories encoding the anomalies of conformal field theories with (2,0) supersymmetry in six dimensions. We explain how the conformal blocks of the (2,0) theories arise in this context. A result of…
We consider a model of directed polymers on regular trees with complex-valued random weights introduced by Cook and Derrida [CD90] and studied mathematically by Derrida, Evans and Speer [DES93]. In addition to the usual weak-disorder and…
The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary…
We introduce a new disorder regime for directed polymers with one space and one time dimension that is accessed by scaling the inverse temperature parameter \beta with the length of the polymer n. We scale \beta_n := \beta n^{-\alpha} for…
It is possible to formulate 2d field theory on the ultrametric space with the free correlators identical to 2d correlators and the same potential. Such model should carry some features of original model for scale invariant theories. For the…
The continuum limit and scaling properties of an asymptotically free field theory regularized on a random lattice are compared with those on a regular square lattice. We work on random lattices parametrized by a degree of ``randomness''…
The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many-body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric…
We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then…
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules. One can construct more general (codimension-one)…
We study two-dimensional conformal field theories generated from a ``symplectic fermion'' - a free two-component fermion field of spin one - and construct the maximal local supersymmetric conformal field theory generated from it. This…
We study random copolymers consisted of two kinds of monomers with attraction between similar kinds. The mean field analysis of this system indicates a continuous phase transition into a phase with periodic microdomain structure. It is…
We present a numerical algorithm to evaluate the self-consistent field theory for melts composed of block copolymers with multiply-branched architecture. We present results for the case of branched copolymers with doubly-functional groups…
We give a review of the theory of random fields defined on the observable part of the Universe that satisfy the cosmological principle, i.e., invariant with respect to the 6-dimensional group $\mathcal{G}$ of the isometries of the time…