Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry

Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy some constraints that bear a similarity with the Hitchin equations, and contain the Donaldson equations as a special subcase. It turns out that these constraints can be obtained by dimensional reduction of the octonionic instanton equations, and may be rephrased in terms of a selfduality-like condition for a complex connection. We also show that the supersymmetry conditions imply the equations of motion only partially.Comment: 29 pages, 3 tables. v2: references added. v3: conclusion extended, version published in JHE

A note on instanton counting for N=2 gauge theories with classical gauge groups

We study the prepotential of N=2 gauge theories using the instanton counting techniques introduced by Nekrasov. For the SO theories without matter we find a closed expression for the full prepotential and its string theory gravitational corrections. For the more subtle case of Sp theories without matter we discuss general features and compute the prepotential up to instanton number three. We also briefly discuss SU theories with matter in the symmetric and antisymmetric representations. We check all our results against the predictions of the corresponding Seiberg-Witten geometries.Comment: 24 pages, LaTeX. v2: refs added. v3: typos correcte

Instanton calculus in R-R background and the topological string

We study a system of fractional D3 and D(-1) branes 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 supergravity. In particular, we analyze the instanton moduli space using string theory methods and 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. We also comment on the relation between our approach and the so-called Omega-background.Comment: 38 pages, 2 figures, JHEP class (included); final version to be pubished in JHE

An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills

We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold singularities. At these singular points in moduli space the theory exhibits a duality cascade and flows to a confining theory with a mass gap. By exactly solving the corresponding holomorphic matrix model we compute the exact quantum superpotential generated at the end of the duality cascade and calculate precisely how quantum effects deform the classical moduli space by replacing the conifold singularities with three-cycles of finite size. Locally the structure is that of the deformed conifold, but the global geometry is different. This desingularized quantum deformed geometry is the moduli space of probe D3-branes at the end of a duality cascade realized on the worldvolume of (fractional) D3-branes placed at the isolated conifold singularities in the deformation of the orbifold C^3/Z_n x Z_n with discrete torsion.Comment: Uses Latex, JHEP.cls, 43 pages, 3 figure

Instantons on Quivers and Orientifolds

We compute the prepotential for gauge theories descending from ${\cal N}=4$ SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge theories with gauge group SO/Sp is also described. In the case with no gravitational corrections the results are shown to be in agreement with Seiberg-Witten analysis and previous results in the literature.Comment: 28 pages, revised version, references added, some typos correcte

Multi-Instanton Calculus and Equivariant Cohomology

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N=4 and N=2 gauge theories with adjoint and fundamental matter.Comment: 29 pages, one more reference adde

Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories

We study IR/UV mixing effects in noncommutative supersymmetric Yang-Mills theories with gauge group U(N) using background field perturbation theory. We compute three- and four-point functions of background fields, and show that the IR/UV mixed contributions to these correlators can be reproduced from an explicitly gauge-invariant effective action, which is expressed in terms of open Wilson lines.Comment: 23 pages, 8 figures. v2: new section and references added, effective action expressed only in terms of open Wilson lines operator

Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions

We explore how the IR pathologies of noncommutative field theory are resolved when the theory is realized as open strings in background B-fields: essentially, since the IR singularities are induced by UV/IR mixing, string theory brings them under control in much the same way as it does the UV singularities. We show that at intermediate scales (where the Seiberg-Witten limit is a good approximation) the theory reproduces the noncommutative field theory with all the (un)usual features such as UV/IR mixing, but that outside this regime, in the deep infra-red, the theory flows continuously to the commutative theory and normal Wilsonian behaviour is restored. The resulting low energy physics resembles normal commutative physics, but with additional suppressed Lorentz violating operators. We also show that the phenomenon of UV/IR mixing occurs for the graviton as well, with the result that, in configurations where Planck's constant receives a significant one-loop correction (for example brane-induced gravity), the distance scale below which gravity becomes non-Newtonian can be much greater than any compact dimensions.Comment: 30 pages. Slight revision: clarified some points and added a referenc

Solving matrix models using holomorphy

We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by holomorphy. It is argued that these quantum deformations give rise to non-trivial relations for generalized resolvents that must hold in the associated matrix model. These relations allow to solve a sector of the associated matrix model in a similar way to a one-matrix model, by studying a curve that encodes the generalized resolvents. At the level of loop equations for the matrix model, the situations with a moduli space can sometimes be considered as a degeneration of an infinite set of linear equations, and the quantum moduli space encodes the consistency conditions for these equations to have a solution.Comment: 38 pages, JHEP style, 1 figur

The DNA Damage Signal for Mdm2 Regulation, Trp53 Induction, and Sunburn Cell Formation In Vivo Originates from Actively Transcribed Genes

The stratum corneum and DNA repair do not completely protect keratinocytes from ultraviolet B. A third defense prevents cells with DNA photoproducts from becoming precancerous mutant cells: apoptosis of ultraviolet-damaged keratinocytes (“sunburn cells”). As signals for ultraviolet-induced apoptosis, some studies implicate DNA photoproducts in actively transcribed genes; other studies implicate non-nuclear signals. We traced and quantitated the in vivo DNA signal through several steps in the apoptosis-signaling pathway in haired mice. Homozygous inactivation of Xpa, Csb, or Xpc nucleotide excision repair genes directed the accumulation of DNA photoproducts to specific genome regions. Repair-defective Xpa−/− mice were 7–10-fold more sensitive to sunburn cell induction than wild-type mice, indicating that 86–90% of the ultraviolet B signal for keratinocyte apoptosis involved repairable photoproducts in DNA; the remainder involves unrepaired DNA lesions or nongenomic targets. Csb−/− mice, defective only in excising photoproducts from actively transcribed genes, were as sensitive as Xpa−/−, indicating that virtually all of the DNA signal originates from photoproducts in active genes. Conversely, Xpc−/− mice, defective in repairing the untranscribed majority of the genome, were as resistant to apoptosis as wild type. Sunburn cell formation requires the Trp53 tumor suppressor protein; 90–96% of the signal for its induction in vivo involved transcribed genes. Mdm2, which regulates the stability of Trp53 through degradation, was induced in vivo by low ultraviolet B doses but was suppressed at erythemal doses. DNA photoproducts in actively transcribed genes were involved in ≈ 89% of the Mdm2 response