29 research outputs found
A new representation for two- and three-point correlators of operators from sl(2) sector
We construct a new representation for two- and three-point correlators of
operators from sl(2) sector of planar N = 4 SYM. The spin and twist of
operators are arbitrary. We start with the correlation function of light-ray
operators and carry out a projection to particular local operators using the
method of Separated Variables. With the same calculation we obtain polynomials
which are dual to wave functions of sl(2,R) spin-chain.Comment: 19 pages, 5 figure
Exact Zero Vacuum Energy in twisted SU(N) Principal Chiral Field
We present a finite set of equations for twisted PCF model. At the special
twist in the root of unity we demonstrate that the vacuum energy is exactly
zero at any size L. Also in SU(2) case we numerically calculate the energy of
the single particle state with zero rapidity, as a function of L.Comment: 5 pages, 3 figure
The Superconformal Xing Equation
Crossing symmetry provides a powerful tool to access the non-perturbative
dynamics of conformal and superconformal field theories. Here we develop the
mathematical formalism that allows to construct the crossing equations for
arbitrary four-point functions in theories with superconformal symmetry of type
I, including all superconformal field theories in dimensions. Our advance
relies on a supergroup theoretic construction of tensor structures that
generalizes an approach which was put forward in \cite{Buric:2019dfk} for
bosonic theories. When combined with our recent construction of the relevant
superblocks, we are able to derive the crossing symmetry constraint in
particular for four-point functions of arbitrary long multiplets in all
4-dimensional superconformal field theories.Comment: 49 page
Three-point correlator of twist-2 light-ray operators in N=4 SYM in BFKL approximation
We present calculation of the correlation function of three twist-2 operators
in the BFKL limit. The calculation is performed in N = 4 SYM but the result is
valid in other gauge theories such as QCD. The obtained leading order structure
constant is exact for any number of colors.Comment: 24 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1506.0203
Three-point correlator of twist-2 operators in BFKL limit
We compute the correlation function of three twist-2 operators in N = 4 SYM
in the leading BFKL approximation at any N_c. In this limit, the result is
applicable to other gauge theories, including QCD.Comment: 5 pages, 2 figures, v2: minor changes, references adde
Superconformal Blocks: General Theory
In this work we launch a systematic theory of superconformal blocks for
four-point functions of arbitrary supermultiplets. Our results apply to a large
class of superconformal field theories including 4-dimensional models with any
number of supersymmetries. The central new ingredient is a
universal construction of the relevant Casimir differential equations. In order
to find these equations, we model superconformal blocks as functions on the
supergroup and pick a distinguished set of coordinates. The latter are chosen
so that the superconformal Casimir operator can be written as a perturbation of
the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent)
term. Solutions to the associated eigenvalue problem can be obtained through a
quantum mechanical perturbation theory that truncates at some finite order so
that all results are exact. We illustrate the general theory at the example of
dimensional theories with supersymmetry for which we
recover known superblocks. The paper concludes with an outlook to 4-dimensional
blocks with supersymmetry.Comment: JHEP format, an appendix and remarks added, typos correcte
Large-N Principal Chiral Model in Arbitrary External Fields
We report the explicit solution for the vacuum state of the two-dimensional
Principal Chiral Model at large- for an arbitrary set of chemical
potentials and any interaction strength, a unique result of such kind for an
asymptotically free QFT. The solution matches one-loop perturbative calculation
at weak coupling, and in the opposite strong-coupling regime exhibits an
emergent spacial dimension from the continuum limit of the Dynkin
diagram.Comment: 5 pages, 1 figur
Two-Point Correlator of Twist-2 Light-Ray Operators in N=SYM in BFKL Approximation
We generalize local operators of the leading twist-2 of = SYM theory to the case of complex Lorentz spin j using principal series representation of sl(2, R). We give the direct computation of correlation function of two such non-local operators in the BFKL regime when j → 1. The correlator appears to have the expected conformal coordinate dependence governed by the anomalous dimension of twist-2 operator in NLO BFKL approximation predicted by Kotikov and Lipatov