93 research outputs found
N=2 Instanton Calculus In Closed String Background
In this contribution we describe how to obtain instanton effects in four
dimensional gauge theories by computing string scattering amplitudes in
D3/D(-1) brane systems. In particular we study a system of fractional D3/D(-1)
branes in a Z_2 orbifold and in a Ramond-Ramond closed string background, and
show that it describes the gauge instantons of N=2 super Yang-Mills theory and
their interactions with the graviphoton of N=2. Using string theory methods we
compute the prepotential of the effective gauge theory exploiting the
localization methods of the instanton calculus, showing that this leads to the
same information given by the topological string.Comment: 12 pages, 2 figures; to appear in the proceedings of 21st
Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics: Noncommutative
Geometry and Quantum Spacetime in Physics, Nishinomiya and Kyoto, Japan,
11-15 Nov 200
Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models
We propose an approach to treat (1+1)--dimensional fermionic systems based on
the idea of algebraic bosonization. This amounts to decompose the elementary
low-lying excitations around the Fermi surface in terms of basic building
blocks which carry a representation of the W_{1+\infty} \times {\overline
W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum
incompressible fluid. This symmetry simply expresses the local particle-number
current conservation at the Fermi surface. The general approach is illustrated
in detail in two examples: the Heisenberg and Calogero-Sutherland models, which
allow for a comparison with the exact Bethe Ansatz solution.Comment: 51 pages, plain LaTe
Deformed N=2 theories, generalized recursion relations and S-duality
We study the non-perturbative properties of N=2 super conformal field
theories in four dimensions using localization techniques. In particular we
consider SU(2) gauge theories, deformed by a generic epsilon-background, with
four fundamental flavors or with one adjoint hypermultiplet. In both cases we
explicitly compute the first few instanton corrections to the partition
function and the prepotential using Nekrasov's approach. These results allow to
reconstruct exact expressions involving quasi-modular functions of the bare
gauge coupling constant and to show that the prepotential terms satisfy a
modular anomaly equation that takes the form of a recursion relation with an
explicitly epsilon-dependent term. We then investigate the implications of this
recursion relation on the modular properties of the effective theory and find
that with a suitable redefinition of the prepotential and of the effective
coupling it is possible, at least up to the third order in the deformation
parameters, to cast the S-duality relations in the same form as they appear in
the Seiberg-Witten solution of the undeformed theory.Comment: 33 pages, no figures, LaTeX2
Non-perturbative aspects of gauge/gravity duality
Recently we provided a microscopic derivation of the exact supergravity
profile for the twisted scalar field emitted by systems of fractional D3-branes
at a Z2 orbifold singularity. In this contribution we focus on a set-up
supporting an N = 2 SYM theory with SU(2) gauge group and Nf=4. We take into
account the tower of D-instanton corrections to the source terms for the
twisted scalar and find that its profile can be expressed in terms of the
chiral ring elements of the gauge theory. We show how the twisted scalar, which
at the perturbative level represents the gravity counterpart of the gauge
coupling, at the non-perturbative level is related to the effective gauge
coupling in an interestingly modified way.Comment: 13 pages, 1 figure. Proceedings of the Corfu Summer Institute 2012
"School and Workshops on Elementary Particle Physics and Gravity", September
8-27, 2012, Corfu, Greece. Luca Giacone was the speaker. v2: two references
added, one reference update
Surface operators in N=2 SQCD and Seiberg Duality
We study half-BPS surface operators in N=2supersymmetric asymptotically
conformal gauge theories in four dimensions with SU(N) gauge group and 2N
fundamental flavours using localization methods and coupled 2d/4d quiver gauge
theories. We show that contours specified by a particular Jeffrey-Kirwan
residue prescription in the localization analysis map to particular
realizations of the surface operator as flavour defects. Seiberg duality of the
2d/4d quivers is mapped to contour deformations of the localization integral
which in this case involves a residue at infinity. This is reflected as a
modified Seiberg duality rule that shifts the Lagrangian of the purported dual
theory by non-perturbative terms. The new rules, that depend on the 4d gauge
coupling, lead to a match between the low energy effective twisted chiral
superpotentials for any pair of dual 2d/4d quivers.Comment: 32 page
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