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Dmytro Volin

Publications and source records attributed to Dmytro Volin.

29 records · Page 2Linked to original sources
arXiv2012

Solving the AdS/CFT Y-system

Using integrability and analyticity properties of the AdS5/CFT4 Y-system we reduce it to a finite set of nonlinear integral equations. The Z4 symmetry of the underlying coset sigma model, in its quantum version, allows for a deeper insight into the analyticity structure of the underlying Y-functions and T-functions, as well as for their analyticity friendly parameterization in terms of Wronskian determinants of Q-functions. As a check for the new equations, we reproduce the numerical results for the Konishi operator previously obtained from the original infinite Y-system.

hep-th↗
arXiv2012

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010.

hep-th↗
arXiv2011

Quantum folded string and integrability: from finite size effects to Konishi dimension

Using the algebraic curve approach we one-loop quantize the folded string solution for the type IIB superstring in AdS(5)xS(5). We obtain an explicit result valid for arbitrary values of its Lorentz spin S and R-charge J in terms of integrals of elliptic functions. Then we consider the limit S ~ J ~ 1 and derive the leading three coefficients of strong coupling expansion of short operators. Notably, our result evaluated for the anomalous dimension of the Konishi state gives 2λ^{1/4}-4+2/λ^{1/4}. This reproduces correctly the values predicted numerically in arXiv:0906.4240. Furthermore we compare our result using some new numerical data from the Y-system for another similar state. We also revisited some of the large S computations using our methods. In particular, we derive finite--size corrections to the anomalous dimension of operators with small J in this limit.

hep-th↗
arXiv2011

String hypothesis for gl(n|m) spin chains: a particle/hole democracy

This paper is devoted to integrable gl(n|m) spin chains which allow for formulation of the string hypothesis. Considering the thermodynamic limit of such spin chains, we derive linear functional equations that symmetricaly treat holes and particles. The functional equations naturally organize different types of excitations into a pattern equivalent to the one of Y-system, and, not surprisingly, the Y-system can be easily derived from the functional equations. The Y-system is known to contain most of the information about the symmetry of the model, therefore we map the symmetry knowledge directly to the description of string excitations. Our analysis is applicable for highest weight representations which for some choice of the Kac-Dynkin diagram have only one nonzero Dynkin label. This generalizes known results for the AdS/CFT spectral problem and for the Hubbard model.

hep-th↗
arXiv2011

From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigma-models

We give an analytical derivation of the mass gap of the O(N) sigma models and investigate a large-order behavior of the weak coupling asymptotic expansion for the energy. For sufficiently large N the series is sign-oscillating, which is expected from the large N solution of the sigma model. However, for N=3 and N=4 the series are sign positive.

hep-th↗
arXiv2010

Quantum integrability and functional equations

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

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arXiv2009

Minimal solution of the AdS/CFT crossing equation

We solve explicitly the crossing equation under sufficiently general assumptions on the structure of the dressing phase. We obtain the BES/BHL dressing phase as a minimal solution of the crossing equation and identify the possible CDD factors.

hep-th↗
arXiv2008

The 2-loop generalized scaling function from the BES/FRS equation

We formulate the BES/FRS equation as a functional equation in the rapidity space and perform its strong coupling expansion in the limit when $\ell=j/4g$ is kept finite. We obtain a result which is consistent with the previous calculations at tree level and one loop and which differs from the two-loop calculation in 0805.4615 by a term singular at $\ell=0$.

hep-th↗
arXiv2008

Functional BES equation

We give a realization of the Beisert, Eden and Staudacher equation for the planar N=4 supersymetric gauge theory whichseems to be particularly useful to study the strong coupling limit. We use a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into to a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotanski. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.

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arXiv2007

Strong coupling limit of Bethe Ansatz equations

We develop a method to analyze the strong coupling limit of the Bethe ansatz equations supposed to give the spectrum of anomalous dimensions of the planar ${\cal N}=4$ gauge theory. This method is particularly adapted for the three rank-one sectors, $su(2)$, $su(1|1)$ and $sl(2)$. We use the elliptic parametrization of the Bethe ansatz variables, which degenerates to a hyperbolic one in the strong coupling limit. We analyze the equations for the highest excited states in the su(2) and $su(1|1)$ sectors and for the state corresponding to the twist-two operator in the $sl(2)$ sector, both without and with the dressing kernel. In some cases we were able to give analytic expressions for the leading order magnon densities. Our method reproduces all existing analytical and numerical results for these states at the leading order.

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