126 research outputs found
The elliptic scattering theory of the 1/2-XYZ and higher order Deformed Virasoro Algebras
Bound state excitations of the spin 1/2-XYZ model are considered inside the
Bethe Ansatz framework by exploiting the equivalent Non-Linear Integral
Equations. Of course, these bound states go to the sine-Gordon breathers in the
suitable limit and therefore the scattering factors between them are explicitly
computed by inspecting the corresponding Non-Linear Integral Equations. As a
consequence, abstracting from the physical model the Zamolodchikov-Faddeev
algebra of two -th elliptic breathers defines a tower of -order Deformed
Virasoro Algebras, reproducing the case the usual well-known algebra of
Shiraishi-Kubo-Awata-Odake \cite{SKAO}.Comment: Latex version, 13 page
Finite -corrections to the SYM prepotential
We derive the first -correction to the instanton partition
functions of Super Yang-Mills (SYM) in four dimensions in the
Nekrasov-Shatashvili limit . In the latter we recall
the emergence of the famous Thermodynamic Bethe Ansatz-like equation which has
been found by Mayer expansion techniques. Here we combine efficiently these to
field theory arguments. In a nutshell, we find natural and resolutive the
introduction of a new operator that distinguishes the singularities
within and outside the integration contour of the partition function.Comment: 13 pages, 1 figur
Quantum integrability of 4d gauge theories
We provide a description of the quantum integrable structure behind the
Thermodynamic Bethe Ansatz (TBA)-like equation derived by Nekrasov and
Shatashvili (NS) for 4d Super Yang-Mills (SYM) theories. In
this regime of the background, -- we shall show --, the instanton partition
function is characterised by the solution of a TQ-equation. Exploiting a
symmetry of the contour integrals expressing the partition function, we derive
a 'dual' TQ-equation, sharing the same T-polynomial with the former. This fact
allows us to evaluate to the quantum Wronskian of two dual solutions (for
) and, then, to reproduce the NS TBA-like equation. The latter acquires
interestingly the deep meaning of a known object in integrability theory, as
its two second determinations give the usual non-linear integral equations
(nlies) derived from the 'dual' Bethe Ansatz equations.Comment: 21 page
Mayer expansion of the Nekrasov pre potential: the subleading -order
The Mayer cluster expansion technique is applied to the Nekrasov instanton
partition function of super Yang-Mills. The
subleading small -correction to the Nekrasov-Shatashvili limiting
value of the prepotential is determined by a detailed analysis of all the
one-loop diagrams. Indeed, several types of contributions can be distinguished
according to their origin: long range interaction or potential expansion,
clusters self-energy, internal structure, one-loop cyclic diagrams, etc.. The
field theory result derived more efficiently in [1], under some minor technical
assumptions, receives here definite confirmation thanks to several remarkable
cancellations: in this way, we may infer the validity of these assumptions for
further computations in the field theoretical approach.Comment: 29 pages, 9 figure
Seiberg-Witten period relations in Omega background
Omega-deformation of the Seiberg-Witten curve is known to be written in terms
of the qq-character, namely the trace of a specific operator acting in a
Hilbert space spanned by certain Young diagrams. We define a differential form
acting on this space and establish two discretised versions of the
Seiberg-Witten expressions for the periods and related relations for the
prepotential.Comment: 19 pages, 1 figur
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