The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN−1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Quantum supersymmetric generalisation of Bogomolnyi bounds

We review here classical Bogomolnyi bounds, and their generalisation to supersymmetric quantum field theories by Witten and Olive. We also summarise some recent work by several people on whether such bounds are saturated in the quantised theory.

Low energy properties of the SU(m|n) supersymmetric Haldane–Shastry spin chain

The ground state and low energy excitations of the SU(m|n) supersymmetric Haldane–Shastry spin chain are analyzed. In the thermodynamic limit, it is found that the ground state degeneracy is finite only for the SU(m|0) and SU(m|1) spin chains, while the dispersion relation for the low energy and low momentum excitations is linear for all values of m and n. We show that the low energy excitations of the SU(m|1) spin chain are described by a conformal field theory of m non-interacting Dirac fermions which have only positive energies; the central charge of this theory is m/2. Finally, for ngreater-or-equal, slanted1, the partition functions of the SU(m|n) Haldane–Shastry spin chain and the SU(m|n) Polychronakos spin chain are shown to be related in a simple way in the thermodynamic limit at low temperatures.

Applications of Gauge/Gravity Duality to QCD and Heavy Ion Collisions

The description of quarks and gluons, using the theory of quantum chromodynamics (QCD), has been known for a long time. Nevertheless, many fundamental questions in QCD remain unanswered. This is mainly due to problems in solving the theory at low energies, where the theory is strongly interacting. AdS/CFT is a duality between a specific string theory and a conformal field theory. Duality provides new tools to solve the conformal field theory in the strong coupling regime. There is also some evidence that using the duality, one can get at least qualitative understanding of how QCD behaves at strong coupling. In this thesis, we try to address some issues related to QCD and heavy ion collisions, applying the duality in various ways.

Non-Abelian chiral gauge theories in two dimensions

An anomalous multiflavor chiral theory, with the gauge group SU(N), is studied using non-Abelian bosonization. The theory can be made gauge invariant by introducing Wess-Zumino fields and it is particularly simple if the Jackiw-Rajaraman parameter equals 2. In the strong-coupling limit, the low-energy effective theory only contains light unconfined fermions which interact weakly.

Witten index of supersymmetric chiral theories

The Witten index can be defined in many supersymmetric theories by formulating them in the space-time R×S3. If the index is nonzero for any value of the radius of S3, it can be shown that the theory does not break supersymmetry in Minkowski space. This approach rules out supersymmetry breaking in a large class of models, chiral and otherwise. The index arguments are consistent with previous instanton calculations which indicate supersymmetry breaking in certain theories.

Sneutrino-antisneutrino oscillations at colliders

Modern elementary particle physics is based on quantum field theories. Currently, our understanding is that, on the one hand, the smallest structures of matter and, on the other hand, the composition of the universe are based on quantum field theories which present the observable phenomena by describing particles as vibrations of the fields. The Standard Model of particle physics is a quantum field theory describing the electromagnetic, weak, and strong interactions in terms of a gauge field theory. However, it is believed that the Standard Model describes physics properly only up to a certain energy scale. This scale cannot be much larger than the so-called electroweak scale, i.e., the masses of the gauge fields W^+- and Z^0. Beyond this scale, the Standard Model has to be modified. In this dissertation, supersymmetric theories are used to tackle the problems of the Standard Model. For example, the quadratic divergences, which plague the Higgs boson mass in the Standard model, cancel in supersymmetric theories. Experimental facts concerning the neutrino sector indicate that the lepton number is violated in Nature. On the other hand, the lepton number violating Majorana neutrino masses can induce sneutrino-antisneutrino oscillations in any supersymmetric model. In this dissertation, I present some viable signals for detecting the sneutrino-antisneutrino oscillation at colliders. At the e-gamma collider (at the International Linear Collider), the numbers of the electron-sneutrino-antisneutrino oscillation signal events are quite high, and the backgrounds are quite small. A similar study for the LHC shows that, even though there are several backrounds, the sneutrino-antisneutrino oscillations can be detected. A useful asymmetry observable is introduced and studied. Usually, the oscillation probability formula where the sneutrinos are produced at rest is used. However, here, we study a general oscillation probability. The Lorentz factor and the distance at which the measurement is made inside the detector can have effects, especially when the sneutrino decay width is very small. These effects are demonstrated for a certain scenario at the LHC.

Gauge-invariant reformulation of theories with second-class constraints

Given a classical dynamical theory with second-class constraints, it is sometimes possible to construct another theory with first-class constraints, i.e., a gauge-invariant one, which is physically equivalent to the first theory. We identify some conditions under which this may be done, explaining the general principles and working out several examples. Field theoretic applications include the chiral Schwinger model and the non-linear sigma model. An interesting connection with the work of Faddeev and Shatashvili is pointed out.

Implication of a Higgs boson at 125 GeV within the stochastic superspace framework

We revisit the issue of considering stochasticity of Grassmannian coordinates in N = 1 superspace, which was analyzed previously by Kobakhidze et al. In this stochastic supersymmetry (SUSY) framework, the soft SUSY breaking terms of the minimal supersymmetric Standard Model (MSSM) such as the bilinear Higgs mixing, trilinear coupling, as well as the gaugino mass parameters are all proportional to a single mass parameter xi, a measure of supersymmetry breaking arising out of stochasticity. While a nonvanishing trilinear coupling at the high scale is a natural outcome of the framework, a favorable signature for obtaining the lighter Higgs boson mass m(h) at 125 GeV, the model produces tachyonic sleptons or staus turning to be too light. The previous analyses took Lambda, the scale at which input parameters are given, to be larger than the gauge coupling unification scale M-G in order to generate acceptable scalar masses radiatively at the electroweak scale. Still, this was inadequate for obtaining m(h) at 125 GeV. We find that Higgs at 125 GeV is highly achievable, provided we are ready to accommodate a nonvanishing scalar mass soft SUSY breaking term similar to what is done in minimal anomaly mediated SUSY breaking (AMSB) in contrast to a pure AMSB setup. Thus, the model can easily accommodate Higgs data, LHC limits of squark masses, WMAP data for dark matter relic density, flavor physics constraints, and XENON100 data. In contrast to the previous analyses, we consider Lambda = M-G, thus avoiding any ambiguities of a post-grand unified theory physics. The idea of stochastic superspace can easily be generalized to various scenarios beyond the MSSM. DOI: 10.1103/PhysRevD.87.035022

SuSeFLAV 1.2: Program for supersymmetric mass spectra with seesaw mechanism and rare lepton flavor violating decays

Accurate supersymmetric spectra are required to confront data from direct and indirect searches of supersymmetry. SuSeFLAV is a numerical tool capable of computing supersymmetric spectra precisely for various supersymmetric breaking scenarios applicable even in the presence of flavor violation. The program solves MSSM RGEs with complete 3 x 3 flavor mixing at 2-loop level and one loop finite threshold corrections to all MSSM parameters by incorporating radiative electroweak symmetry breaking conditions. The program also incorporates the Type-I seesaw mechanism with three massive right handed neutrinos at user defined mass scales and mixing. It also computes branching ratios of flavor violating processes such as l(j) -> l(i)gamma, l(j) -> 3 l(i), b -> s gamma and supersymmetric contributions to flavor conserving quantities such as (g(mu) - 2). A large choice of executables suitable for various operations of the program are provided. Program summary Program title: SuSeFLAV Catalogue identifier: AEOD_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEOD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 76552 No. of bytes in distributed program, including test data, etc.: 582787 Distribution format: tar.gz Programming language: Fortran 95. Computer: Personal Computer, Work-Station. Operating system: Linux, Unix. Classification: 11.6. Nature of problem: Determination of masses and mixing of supersymmetric particles within the context of MSSM with conserved R-parity with and without the presence of Type-I seesaw. Inter-generational mixing is considered while calculating the mass spectrum. Supersymmetry breaking parameters are taken as inputs at a high scale specified by the mechanism of supersymmetry breaking. RG equations including full inter-generational mixing are then used to evolve these parameters up to the electroweak breaking scale. The low energy supersymmetric spectrum is calculated at the scale where successful radiative electroweak symmetry breaking occurs. At weak scale standard model fermion masses, gauge couplings are determined including the supersymmetric radiative corrections. Once the spectrum is computed, the program proceeds to various lepton flavor violating observables (e.g., BR(mu -> e gamma), BR(tau -> mu gamma) etc.) at the weak scale. Solution method: Two loop RGEs with full 3 x 3 flavor mixing for all supersymmetry breaking parameters are used to compute the low energy supersymmetric mass spectrum. An adaptive step size Runge-Kutta method is used to solve the RGEs numerically between the high scale and the electroweak breaking scale. Iterative procedure is employed to get the consistent radiative electroweak symmetry breaking condition. The masses of the supersymmetric particles are computed at 1-loop order. The third generation SM particles and the gauge couplings are evaluated at the 1-loop order including supersymmetric corrections. A further iteration of the full program is employed such that the SM masses and couplings are consistent with the supersymmetric particle spectrum. Additional comments: Several executables are presented for the user. Running time: 0.2 s on a Intel(R) Core(TM) i5 CPU 650 with 3.20 GHz. (c) 2012 Elsevier B.V. All rights reserved.

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be mu h/4 pi k(B), when h and k(B) are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In,addition, certain optically thin, hot, accretion flows, of temperature greater than or similar to 10(9) K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.

Beam polarization effects in the radiative production of lightest neutralinos in e(+)e(-) collisions in supersymmetric grand unified models

We study the production of the lightest neutralinos in the process e(+)e(-) -> chi(0)(1)chi(0)(1)gamma in supersymmetric grand unified models for the International Linear Collider energies with longitudinally polarized beams. We consider cases where the standard model gauge group is unified into the grand unified gauge groups SU(5), or SO(10). We have carried out a comprehensive study of this process in the SU(5) and SO(10) grand unified theories which includes the QED radiative corrections. We compare and contrast the dependence of the signal cross section on the grand unified gauge group, and on the different representations of the grand unified gauge group, when the electron and positron beams are longitudinally polarized. To assess the feasibility of experimentally observing the radiative production process, we have also considered in detail the background to this process coming from the radiative neutrino production process e(+)e(-)-> nu(nu) over bar gamma with longitudinally polarized electron and positron beams. In addition we have also considered the supersymmetric background coming from the radiative production of scalar neutrinos in the process e(+)e(-) -> (nu) over tilde(nu) over tilde*gamma with longitudinally polarized beams. The process can be a major background to the radiative production of neutralinos when the scalar neutrinos decay invisibly.

Feshbach resonance in a synthetic non-Abelian gauge field

We study the Feshbach resonance of spin-1/2 particles in a uniform synthetic non-Abelian gauge field that produces spin-orbit coupling and constant spin potentials. We develop a renormalizable quantum field theory including the closed-channel boson which engenders the resonance. We show that the gauge field shifts the Feshbach field where the low-energy scattering length diverges. In addition the Feshbach field is shown to depend on the center-of-mass momentum of the particles. For high-symmetry gauge fields which produce a Rashba spin coupling, we show that the system supports two bound states over a regime of magnetic fields when the background scattering length is negative and the resonance width is comparable to the energy scale of the spin-orbit coupling. We discuss interesting consequences useful for future theoretical and experimental studies, even while our predictions are in agreement with recent experiments.