Related papers: A Lattice Formulation of Two Dimensional Topologic…
The constraints of $BF$ topological gauge theories are used to construct Hamiltonians which are anti-commutators of the BRST and anti-BRST operators. Such Hamiltonians are a signature of Topological Quantum Field Theories (TQFT's). By…
We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree…
Recent proposals for the Symmetry Topological Field Theory (SymTFT) of Maxwell theory admit a 0-form symmetry compatible with the classical $SL_2(\mathbb{R})$ duality of electromagnetism. We describe how to realize these automorphisms of…
A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…
Symmetry Theories (SymThs) provide a flexible framework for analyzing the global categorical symmetries of a $D$-dimensional QFT$_{D}$ in terms of a $(D+1)$-dimensional bulk system SymTh$_{D+1}$. In QFTs realized via local string…
We have proposed a lattice SUSY formulation which we may call super doubler approach, where chiral fermion species doublers and their bosonic counter parts are either identified as super partners or truncated by chiral conditions. We claim…
We propose a manifestly supersymmetric formulation of the Symmetry Topological Field Theory (SuSymTFT) for theories with supersymmetry. The SymTFT is a framework that helps organizing symmetries and anomalies of a QFT. Albeit a lot of…
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the…
We study two-dimensional non-abelian BF theory in Lorenz gauge and prove that it is a topological conformal field theory. This opens the possibility to compute topological string amplitudes (Gromov-Witten invariants). We found that the…
We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge…
We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We…
We continue our exploration of exotic, gapless lattice and continuum field theories with subsystem global symmetries. In an earlier paper, we presented free lattice models enjoying all the global symmetries (except continuous translations),…
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…
We perform the Becchi-Rouet-Stora-Tyutin (BRST) analysis of the Freedman-Townsend (FT) model of topologically massive non-Abelian theory by exploiting its (1-form) Yang-Mills (YM) gauge transformations to show the existence of some novel…
We investigate (2+1)-d Hamiltonian lattice gauge theory using a class of Hamiltonians having exactly known vacuum states. These theories are shown to have a wide range of possible classical continuum limits which differ from that of the…
In a Hermitian system, bound states must have quantized energies, whereas extended states can form a continuum. We demonstrate how this principle fails for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians with an…
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…
Using the duality between seemingly different (2+1)d conformal field theories (CFT) proposed recently, we study a series of (2+1)d stable self-dual interacting CFTs. These CFTs can be realized (for instance) on the boundary of the (3+1)d…
A gauge theory with 4 physical dimensions can be consistently expressed as a renormalizable topological quantum field theory in 5 dimensions. We extend the symmetries in the 5-dimensional framework to include not only a topological BRST…
The derivation of the exact and unique nilpotent Becchi-Rouet-Stora-Tyutin (BRST)- and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of…