121,955 research outputs found
N = 2 Conformal SYM theories at large N
No full textWe consider a class of N = 2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere S4, which also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-N limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach
and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with N differs in the planar limit from the N = 4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small 't Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic
investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed
A matrix-model approach to integrated correlators in a N=2 SYM theory
No full textIn a N = 2 superconformal gauge theory with matter hypermultiplets transforming in the symmetric and anti-symmetric representations of SU(N), we study the integrated correlators of two Coulomb-branch operators and two moment-map operators using localization. In the corresponding matrix model we identify the operator associated with the integrated insertions of moment-map operators and provide for it an exact expression valid for all values of the coupling constant in the planar limit. This allows us to study the integrated correlators at strong-coupling where we show that they behave as the 2-point functions of the Coulomb-branch operators, up to an overall constant dependent only on the conformal dimensions of the latter. The strong-coupling relation between integrated correlators and
2-point functions turns out to be the same as in N = 4 SYM at large N, despite the reduced amount of supersymmetry in our theory
N = 2 Conformal SYM theories at large N
No full textWe consider a class of N = 2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere S4, which also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-N limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with N differs in the planar limit from the N = 4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small ’t Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed
Integrated correlators with a Wilson line in N= 4 SYM
No full textIn the context of integrated correlators in N= 4 SYM, we study the 2-point functions of local operators with a superconformal line defect. Starting from the mass-deformed N= 2* theory in presence of a 1/2-BPS Wilson line, we exploit the residual superconformal symmetry after the defect insertion, and show that the massive deformation corresponds to integrated insertions of the superconformal primaries belonging to the stress tensor multiplet with a specific integration measure which is explicitly derived after enforcing the superconformal Ward identities. Finally, we show how the Wilson line integrated correlator can be computed by the N= 2* Wilson loop vacuum expectation value on a 4-sphere in terms of a matrix model using supersymmetric localization. In particular, we reformulate previous matrix model computations by making use of recursion relations and Bessel kernels, providing a direct link with more general localization computations in N= 2 theories
Localization vs holography in quiver theories
No full textWe study 4-dimensional superconformal quiver gauge theories
obtained with an orbifold projection from SYM, and compute the
2- and 3-point correlation functions among chiral/anti-chiral single-trace
scalar operators and the corresponding structure constants. Exploiting
localization, we map the computation to an interacting matrix model and obtain
expressions for the correlators and the structure constants that are valid for
any value of the 't Hooft coupling in the planar limit of the theory. At strong
coupling, these expressions simplify and allow us to extract the leading
behavior in an analytic way. Finally, using the AdS/CFT correspondence, we
compute the structure constants from the dual supergravity theory and obtain
results that perfectly match the strong-coupling predictions from localization.Comment: 51 pages, 5 figure
S-duality and the prepotential of N=2* theories (I): the ADE algebras
No full textThe prepotential of N=2* supersymmetric theories with unitary gauge groups in an Omega-background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality acts on the prepotential as a Fourier transform we generalise this result to N=2* theories with gauge algebras of the D and E type and show that their prepotentials can be written in terms of quasi-modular forms of SL(2,Z). The results are checked against microscopic multi-instanton calculus based on localization for the A and D series and reproduce the known 1-instanton prepotential of the pure N=2 theories for any gauge group of ADE type. Our results can also be used to obtain the multi-instanton terms in the exceptional theories for which the microscopic instanton calculus and the ADHM construction are not available
S-duality and the prepotential in N=2* theories (II): the non-simply laced algebras
No full textWe derive a modular anomaly equation satisfied by the prepotential of the N=2* supersymmetric theories with non-simply laced gauge algebras, including the classical B and C infinite series and the exceptional F4 and G2 cases. This equation determines the exact prepotential recursively in an expansion for small mass in terms of quasi-modular forms of the S-duality group. We also discuss the behaviour of these theories under S-duality and show that the prepotential of the SO(2r+1) theory is mapped to that of the Sp(2r) theory and viceversa, while the exceptional F4 and G2 theories are mapped into themselves (up to a rotation of the roots) in analogy with what happens for the N=4 supersymmetric theories. These results extend the analysis for the simply laced groups presented in a companion paper
N = 1/2 Gauge Theory And Its Instanton Moduli Space From Open Strings In RR Background
No full textWe derive the four dimensional N=1/2 super Yang-Mills theory from tree-level computations in RNS open string theory with insertions of closed string Ramond-Ramond vertices. We also study instanton configurations in this gauge theory and their ADHM moduli space, using systems of D3 and D(-1) branes in a R-R background
Instanton effects in N=1 brane models and the Kahler metric of twisted matter
No full textWe consider locally consistent systems of magnetized D9 branes on an orbifolded six-torus which support N=1 gauge theories. In such realizations, the matter multiplets arise from "twisted" strings connecting different stacks of branes. The introduction of Euclidean 5 branes (E5) wrapped on the six-dimensional compact space leads to instanton effects. For instance, if the system is engineered so as to yield SQCD, a single E5 brane may account for the ADS/TVY superpotential. We discuss the subtle interplay that exists between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy action of the N=1 theory. The consistency of this picture allows to obtain information on the Kahler metric of the chiral matter multiplets arising from twisted strings
R-SYMMETRY AND THE TOPOLOGICAL TWIST OF N=2 EFFECTIVE SUPERGRAVITIES OF HETEROTIC STRINGS
No full textWe discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable off-shell R-symmetry exists which can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds ST(n)=SU(1,1)/U(1)\times SO(2,n)/SO(2) \times SO(n) R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds {\hat {ST}}(n) a discrete R-symmetry is sufficient and we argue that it exists.We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable off-shell R-symmetry exists which can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds a discrete R-symmetry is sufficient and we argue that it exists
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