Related papers: Renormalisation and the Batalin-Vilkovisky formali…
The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with inverse mass parameter, in addition to a possible topological mass term. The novelty is that the…
We provide Wilsonian proof for renormalizability of four-dimensional quantum field theories with ${\cal N}=1/2$ supersymmetry. We argue that the non-hermiticity inherent to these theories permits assigning noncanonical scaling dimension…
In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation techniques applied to families of CQFT's labelled by finite…
The partition function of complex Chern-Simons theory on a 3-manifold with torus boundary reduces to a finite dimensional state-integral which is a holomorphic function of a complexified Planck's constant $\tau$ in the complex cut plane and…
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially…
We describe special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight-folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles…
We give a proof of perturbative renormalizability of SU(2) Yang--Mills theory in four-dimensional Euclidean space which is based on the Flow Equations of the renormalization group. The main motivation is to present a proof which does not…
There is a large mathematical literature on classical mechanics and field theory, especially on the relationship to symplectic geometry. One might think that the classical Chern-Simons theory, which is topological and so has vanishing…
We introduce an unrolled quantization $U_q^E(\mathfrak{gl}(1 \vert 1))$ of the complex Lie superalgebra $\mathfrak{gl}(1 \vert 1)$ and use its categories of weight modules to construct and study new three dimensional non-semisimple…
We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4,…
We provide N=1 Super Yang-Mills theory in the Wess-Zumino gauge with mass terms for the supersymmetric partners of the gauge fields and of the matter fields, together with a supersymmetric mass term for the fermionic matter fields. All mass…
We study renormalizability aspects of the spectral action for the Yang-Mills system on a flat 4-dimensional background manifold, focusing on its asymptotic expansion. Interpreting the latter as a higher-derivative gauge theory, a…
We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the…
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in…
We consider the deformations of a supersymmetric quantum field theory by adding spacetime-dependent terms to the action. We propose to describe the renormalization of such deformations in terms of some cohomological invariants, a class of…
We calculate $q$-dimension of $k$-th Cartan power of fundamental representation $\Lambda_0$, corresponding to affine root of affine simply laced Kac-Moody algebras, and show that in the limit $q\rightarrow 1 $, and with natural…
A quantization procedure for the Yang-Mills equations for the Minkowski space $\mathbf{R}^{1,3}$ is carried out in such a way that field maps satisfying Wightman axioms of Constructive Quantum Field Theory can be obtained. Moreover, by…
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamitonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of…
A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number ($k$) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em all} $k$…
The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR…