BGWM as Second Constituent of Complex Matrix Model

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).Comment: 42 page

Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling

We use the AdS/CFT prescription of Alday and Maldacena \cite{am} to analyze gluon 6-point scattering amplitudes at strong coupling in ${\cal N}=4$ SYM. By cutting and gluing we obtain AdS 6-point amplitudes that contain extra boundary conditions and come close to matching the field theory results. We interpret them as parts of the field theory amplitudes, containing only certain diagrams. We also analyze the collinear limits of 6- and 5-point amplitudes and discuss the results.Comment: 35 pages, 7 figures, latex, references adde

Comments on gluon scattering amplitudes via AdS/CFT

In this article we consider n gluon color ordered, planar amplitudes in N=4 super Yang Mills at strong 't Hooft coupling. These amplitudes are approximated by classical surfaces in AdS_5 space. We compute the value of the amplitude for a particular kinematic configuration for a large number of gluons and find that the result disagrees with a recent guess for the exact value of the amplitude. Our results are still compatible with a possible relation between amplitudes and Wilson loops. In addition, we also give a prescription for computing processes involving local operators and asymptotic states with a fixed number of gluons. As a byproduct, we also obtain a string theory prescription for computing the dual of the ordinary Wilson loop, Tr P exp[ i\oint A ], with no couplings to the scalars. We also evaluate the quark-antiquark potential at two loops.Comment: 27 pages, 9 figures,v3:minor correction

Supersymmetry and Integrability in Planar Mechanical Systems

We present an N=2-supersymmetric mechanical system whose bosonic sector, with two degrees of freedom, stems from the reduction of an SU(2) Yang-Mills theory with the assumption of spatially homogeneous field configurations and a particular ansatz imposed on the gauge potentials in the dimensional reduction procedure. The Painleve test is adopted to discuss integrability and we focus on the role of supersymmetry and parity invariance in two space dimensions for the attainment of integrable or chaotic models. Our conclusion is that the relationships among the parameters imposed by supersymmetry seem to drastically reduce the number of possibilities for integrable interaction potentials of the mechanical system under consideration.Comment: 20 pages, 3 figure

Constructing Gauge Theory Geometries from Matrix Models

We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.Comment: 52 page

Exact 2-point function in Hermitian matrix model

J. Harer and D. Zagier have found a strikingly simple generating function for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.Comment: 31 pages, 1 figur

Euler-Calogero-Moser system from SU(2) Yang-Mills theory

The relation between SU(2) Yang-Mills mechanics, originated from the 4-dimensional SU(2) Yang-Mills theory under the supposition of spatial homogeneity of the gauge fields, and the Euler-Calogero-Moser model is discussed in the framework of Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: due to the gauge invariance and due to the discrete symmetry. In the former case, it is shown that after elimination of the gauge degrees of freedom from the SU(2) Yang-Mills mechanics the resulting unconstrained system represents the ID_3 Euler-Calogero-Moser model with an external fourth-order potential. Whereas in the latter, the IA_6 Euler-Calogero-Moser model embedded in an external potential is derived whose projection onto the invariant submanifold through the discrete symmetry coincides again with the SU(2) Yang-Mills mechanics. Based on this connection, the equations of motion of the SU(2) Yang-Mills mechanics in the limit of the zero coupling constant are presented in the Lax form.Comment: Revtex, 14 pages, no figures. Abstract changed, strata analysis have been included, typos corrected, references adde

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Measurement of the Lambda(b) cross section and the anti-Lambda(b) to Lambda(b) ratio with Lambda(b) to J/Psi Lambda decays in pp collisions at sqrt(s) = 7 TeV

The Lambda(b) differential production cross section and the cross section ratio anti-Lambda(b)/Lambda(b) are measured as functions of transverse momentum pt(Lambda(b)) and rapidity abs(y(Lambda(b))) in pp collisions at sqrt(s) = 7 TeV using data collected by the CMS experiment at the LHC. The measurements are based on Lambda(b) decays reconstructed in the exclusive final state J/Psi Lambda, with the subsequent decays J/Psi to an opposite-sign muon pair and Lambda to proton pion, using a data sample corresponding to an integrated luminosity of 1.9 inverse femtobarns. The product of the cross section times the branching ratio for Lambda(b) to J/Psi Lambda versus pt(Lambda(b)) falls faster than that of b mesons. The measured value of the cross section times the branching ratio for pt(Lambda(b)) > 10 GeV and abs(y(Lambda(b))) < 2.0 is 1.06 +/- 0.06 +/- 0.12 nb, and the integrated cross section ratio for anti-Lambda(b)/Lambda(b) is 1.02 +/- 0.07 +/- 0.09, where the uncertainties are statistical and systematic, respectively.Comment: Submitted to Physics Letters