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Four-point functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory are studied using N=2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar…
We perform a systematic study of flavor-diagonal parity- and time-reversal-violating operators of dimension six which could arise from physics beyond the SM. We begin at the unknown high-energy scale where these operators originate. At this…
In the paper we study the Yang-Mills effective action in the four-dimensional space-time by using background field formalism. We give an explicit way of cutoff regularization procedure, then do a two-loop renormalization and calculate a…
Leading-twist operators have a remarkable property that their divergence vanishes in a free theory. Recently it was suggested that this property can be used for an alternative technique to calculate anomalous dimensions of leading-twist…
We employ the light-cone formalism to construct in the (super) Yang-Mills theories in the multi-color limit the one-loop dilatation operator acting on single trace products of chiral superfields separated by light-like distances. In the N=4…
We study dimension-seven operators in standard model effective field theory. These operators are classified into two sets, one violating lepton number but preserving baryon number ($\Delta L=\pm 2$, $\Delta B=0$) and the other violating…
Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…
A novel method to treat effects from evanescent operators in next-to-leading order (NLO) computations is introduced. The approach allows, besides further simplifications, to discard evanescent-to-physical mixing contributions in NLO…
We look for chiral primaries in the general Leigh-Strassler deformed N=4 super Yang-Mills theory by systematically computing the planar one-loop anomalous dimension for single trace operators up to dimension six. The operators are organised…
We study the leading irrelevant operators along the flat directions of certain supersymmetric theories. In particular, we focus on finite N=2 (including N=4) supersymmetric field theories in four dimensions and show that these operators are…
We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory and multi-scale analysis via inductive…
The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal SU(2,2|N) symmetry should possess universal integrability properties for different N. We provide further support for this…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
The radiative correction to beta function is comprehensively studied at 1 loop in the context of universal extra dimensions. Instead of using cutoffs to regularize 1-loop divergences, the dimensional regularization scheme is used. Large…
We consider an analog of the problem Veblen formulated in 1928 at the IMC: classify invariant differential operators between "natural objects" (spaces of either tensor fields, or jets, in modern terms) over a real manifold of any dimension.…
We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find…
The presence of an infinite number of marginal four-fermion operators is a key characteristic of the two-dimensional Gross-Neveu model. In this study, we investigate the structure of UV divergences in this model, and by symmetry argument we…
We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su$(2|3)$ sector of ${\cal N}=4$ super Yang-Mills theory, have a bare dimension $\sim N$ and are a linear…
A Wheeler-Dewitt quantum constraint operator for four-dimensional, non-perturbative Lorentzian vacuum quantum gravity is defined in the continuum. The regulated Wheeler-DeWitt constraint operator is densely defined, does not require any…
Instanton contributions to the anomalous dimensions of gauge-invariant composite operators in the N=4 supersymmetric SU(N) Yang-Mills theory are studied in the one-instanton sector. Independent sets of scalar operators of bare dimension 2,…