145 research outputs found
The Omega Deformation, Branes, Integrability, and Liouville Theory
We reformulate the Omega-deformation of four-dimensional gauge theory in a
way that is valid away from fixed points of the associated group action. We use
this reformulation together with the theory of coisotropic A-branes to explain
recent results linking the Omega-deformation to integrable Hamiltonian systems
in one direction and Liouville theory of two-dimensional conformal field theory
in another direction.Comment: 96 p
The Omega Deformation From String and M-Theory
We present a string theory construction of Omega-deformed four-dimensional
gauge theories with generic values of \epsilon_1 and \epsilon_2. Our solution
gives an explicit description of the geometry in the core of Nekrasov and
Witten's realization of the instanton partition function, far from the
asymptotic region of their background. This construction lifts naturally to
M-theory and corresponds to an M5-brane wrapped on a Riemann surface with a
selfdual flux. Via a 9-11 flip, we finally reinterpret the Omega deformation in
terms of non-commutative geometry. Our solution generates all modified
couplings of the \Omega-deformed gauge theory, and also yields a geometric
origin for the quantum spectral curve of the associated quantum integrable
system.Comment: LaTeX, 35 pages, 1 figure. Appendix on couplings of hypermultiplets
in N=4 SYM adde
String theory of the Omega deformation
In this article, we construct a supersymmetric real mass deformation for the
adjoint chiral multiplets in the gauge theory describing the dynamics of a
stack of D2-branes in type II string theory. We do so by placing the D2-branes
into the T-dual of a supersymmetric NS fluxbrane background. We furthermore
note that this background is the string theoretic realization of an
Omega-deformation of flat space in the directions transverse to the branes
where the deformation parameters satisfy \epsilon_1 = - \epsilon_2. This
\Omega-deformation therefore serves to give supersymmetric real masses to the
chiral multiplets of the 3D gauge theory. To illustrate the physical effect of
the real mass term, we derive BPS-saturated classical solutions for the branes
rotating in this background. Finally, we reproduce all the same structure in
the presence of NS fivebranes and comment on the relationship to the gauge
theory/spin-chain correspondence of Nekrasov and Shatashvili.Comment: 36 pages. References added, brane construction clarified, edited for
styl
Kinks in the dispersion of strongly correlated electrons
The properties of condensed matter are determined by single-particle and
collective excitations and their interactions. These quantum-mechanical
excitations are characterized by an energy E and a momentum \hbar k which are
related through their dispersion E_k. The coupling of two excitations may lead
to abrupt changes (kinks) in the slope of the dispersion. Such kinks thus carry
important information about interactions in a many-body system. For example,
kinks detected at 40-70 meV below the Fermi level in the electronic dispersion
of high-temperature superconductors are taken as evidence for phonon or
spin-fluctuation based pairing mechanisms. Kinks in the electronic dispersion
at binding energies ranging from 30 to 800 meV are also found in various other
metals posing questions about their origins. Here we report a novel, purely
electronic mechanism yielding kinks in the electron dispersions. It applies to
strongly correlated metals whose spectral function shows well separated Hubbard
subbands and central peak as, for example, in transition metal-oxides. The
position of the kinks and the energy range of validity of Fermi-liquid (FL)
theory is determined solely by the FL renormalization factor and the bare,
uncorrelated band structure. Angle-resolved photoemission spectroscopy (ARPES)
experiments at binding energies outside the FL regime can thus provide new,
previously unexpected information about strongly correlated electronic systems.Comment: 8 pages, 5 figure
A & B model approaches to surface operators and Toda theories
It has recently been argued by Alday et al that the inclusion of surface
operators in 4d N=2 SU(2) quiver gauge theories should correspond to insertions
of certain degenerate operators in the dual Liouville theory. So far only the
insertion of a single surface operator has been treated (in a semi-classical
limit). In this paper we study and generalise this proposal. Our approach
relies on the use of topological string theory techniques. On the B-model side
we show that the effects of multiple surface operator insertions in 4d N=2
gauge theories can be calculated using the B-model topological recursion
method, valid beyond the semi-classical limit. On the mirror A-model side we
find by explicit computations that the 5d lift of the SU(N) gauge theory
partition function in the presence of (one or many) surface operators is equal
to an A-model topological string partition function with the insertion of (one
or many) toric branes. This is in agreement with an earlier proposal by Gukov.
Our A-model results were motivated by and agree with what one obtains by
combining the AGT conjecture with the dual interpretation in terms of
degenerate operators. The topological string theory approach also opens up new
possibilities in the study of 2d Toda field theories.Comment: 43 pages. v2: Added references, including a reference to unpublished
work by S.Gukov; minor changes and clarifications
Gauge Theory Wilson Loops and Conformal Toda Field Theory
The partition function of a family of four dimensional N=2 gauge theories has
been recently related to correlation functions of two dimensional conformal
Toda field theories. For SU(2) gauge theories, the associated two dimensional
theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case
the relation has been extended showing that the expectation value of gauge
theory loop operators can be reproduced in Liouville theory inserting in the
correlators the monodromy of chiral degenerate fields. In this paper we study
Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental
representation of the gauge group and show that they are associated to
monodromies of a certain chiral degenerate operator of A_{N-1} Toda field
theory. The orientation of the curve along which the monodromy is evaluated
selects between fundamental and anti-fundamental representation. The analysis
is performed using properties of the monodromy group of the generalized
hypergeometric equation, the differential equation satisfied by a class of four
point functions relevant for our computation.Comment: 17 pages, 3 figures; references added
Non-Perturbative Topological Strings And Conformal Blocks
We give a non-perturbative completion of a class of closed topological string
theories in terms of building blocks of dual open strings. In the specific case
where the open string is given by a matrix model these blocks correspond to a
choice of integration contour. We then apply this definition to the AGT setup
where the dual matrix model has logarithmic potential and is conjecturally
equivalent to Liouville conformal field theory. By studying the natural
contours of these matrix integrals and their monodromy properties, we propose a
precise map between topological string blocks and Liouville conformal blocks.
Remarkably, this description makes use of the light-cone diagrams of closed
string field theory, where the critical points of the matrix potential
correspond to string interaction points.Comment: 36 page
Classical conformal blocks from TBA for the elliptic Calogero-Moser system
The so-called Poghossian identities connecting the toric and spherical
blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for
the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain
expressions for the classical 4-point block on the sphere. The main motivation
for this line of research is the longstanding open problem of uniformization of
the 4-punctured Riemann sphere, where the 4-point classical block plays a
crucial role. It is found that the obtained representation for certain 4-point
classical blocks implies the relation between the accessory parameter of the
Fuchsian uniformization of the 4-punctured sphere and the eCMY functional.
Additionally, a relation between the 4-point classical block and the ,
twisted superpotential is found and further used to re-derive the
instanton sector of the Seiberg-Witten prepotential of the , supersymmetric gauge theory from the classical block.Comment: 25 pages, no figures, latex+JHEP3, published versio
Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
Recently Alday and Tachikawa proposed a relation between conformal blocks in
a two-dimensional theory with affine sl(2) symmetry and instanton partition
functions in four-dimensional conformal N=2 SU(2) quiver gauge theories in the
presence of a certain surface operator. In this paper we extend this proposal
to a relation between conformal blocks in theories with affine sl(N) symmetry
and instanton partition functions in conformal N=2 SU(N) quiver gauge theories
in the presence of a surface operator. We also discuss the extension to
non-conformal N=2 SU(N) theories.Comment: 40 pages. v2: minor changes and clarification
- âŠ