arXiv subjects

G. W. Semenoff

Publications and source records attributed to G. W. Semenoff.

At least 37 records · Page 2Linked to original sources

arXiv2000

Matrix Theory Interpretation of DLCQ String Worldsheets

We study the null compactification of type-IIA-string perturbation theory at finite temperature. We prove a theorem about Riemann surfaces establishing that the moduli spaces of infinite-momentum-frame superstring worldsheets are identical to those of branched-cover instantons in the matrix-string model conjectured to describe M-theory. This means that the identification of string degrees of freedom in the matrix model proposed by Dijkgraaf, Verlinde and Verlinde is correct and that its natural generalization produces the moduli space of Riemann surfaces at all orders in the genus expansion.

hep-th↗

arXiv2000

Wilson Loops in N=4 Supersymmetric Yang--Mills Theory

Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, $ \sim\exp((constant)\sqrt{g^2N})$. For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of $\sqrt{g^2N}$ also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order $g^4N^2$.

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arXiv1999

Static Potential in N=4 Supersymmetric Yang-Mills Theory

We compute the leading order perturbative correction to the static potential in ${\cal N}=4$ supersymmetric Yang-Mills theory. We show that the perturbative expansion contains infrared logarithms which, when resummed, become logarithms of the coupling constant. The resulting correction goes in the right direction to match the strong coupling behavior obtained from the AdS/CFT correspondence. We find that the strong coupling extrapolation of the sum of ladder diagrams goes as $\sqrt{g^2N}$, as in the supergravity approach.

hep-th↗

arXiv1999

Structure of the Electric Flux in N=4 Supersymmetric Yang-Mills Theory

Correlators of Wilson loop operators with O_4=Tr(F_{μν}^2+...) are computed in N=4 super-Yang-Mills theory using the AdS/CFT correspondence. The results are compared with the leading order perturbative computations. As a consequence of conformal invariance, these correlators have identical forms in the weak and strong coupling limits for circular loops. They are essentially different for contours not protected by conformal symmetry.

hep-th↗

arXiv1999

Universality and the magnetic catalysis of chiral symmetry breaking

The hypothesis that the magnetic catalysis of chiral symmetry breaking is due to interactions of massless fermions in their lowest Landau level is examined in the context of chirally symmetric models with short ranged interactions. It is argued that, when the magnetic field is sufficiently large, even an infinitesimal attractive interaction in the appropriate channel will break chiral symmetry.

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arXiv1999

Quantum Spin-1/2 Antiferromagnetic Chains and Strongly Coupled Multiflavor Schwinger Models

We review the correspondence between strongly coupled lattice multiflavor Schwinger models and SU(N) antiferromagnetic chains. We show that finding the low lying states of the gauge models is equivalent to solving an SU(N) Heisenberg antiferromagnetic chain. For the two-flavor lattice Schwinger model the massless excitations correspond to gapless states of the Heisenberg chain, while the massive states are created by fermion transport in the ground state of the spin chain. Our analysis shows explicitly how spinons may arise in lattice gauge theories.

hep-lat↗

arXiv1999

Solitons on Branes

We examine the possibility that gauge field configurations on stacks of parallel Dp branes support topological solitons. We give an exhaustive list of possible soliton charges for p<7. We also discuss how configurations carrying the soliton charges can be constructed from intersecting branes.

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arXiv1999

Screening and D-brane Dynamics in Finite Temperature Superstring Theory

The thermal dynamics of D-branes and of open superstrings in background gauge fields is studied. It is shown that D-brane dynamics forbids constant velocity motion at finite temperature. T-duality is used to interpret this feature as a consequence of the absence of an equilibrium state of charged strings at finite temperature in a constant background electric field, as a result of Debye screening of electric fields. The effective action for the Polyakov loop operator is computed and the corresponding screening solutions are described. The finite temperature theory is also used to illustrate the importance of carefully incorporating Wu-Yang terms into the string path integral for compact target spaces.

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arXiv1998

Universality in Effective Strings

We demonstrate that, due to the finite thickness of domain walls, and the consequent ambiguity in defining their locations, the effective string description obtained by integrating out bulk degrees of freedom contains ambiguities in the coefficients of the various geometric terms. The only term with unambiguous coefficient is the zeroth order Nambu-Goto term. We argue that fermionic ghost fields which implement gauge-fixing act to balance these ambiguities. The renormalized string tension, obtained after integrating out both bulk and world-sheet degrees of freedom, can be defined in a scheme independent manner; and we compute the explicit finite expressions, to one-loop, for the case of compact quantum electrodynamics and phi-4 theory.

hep-ph↗

arXiv1998

Thermodynamics of D0-branes in matrix theory

We examine the matrix theory representation of D0-brane dynamics at finite temperature. In this case, violation of supersymmetry by temperature leads to a non-trivial static potential between D0-branes at any finite temperature. We compute the static potential in the 1-loop approximation and show that it is short-ranged and attractive. We compare the result with the computations in superstring theory. We show that thermal states of D0-branes can be reproduced by matrix theory only when certain care is taken in integration over the moduli space of classical solutions in compactified time.

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arXiv1998

Characterizing Phases of the non-Abelian Coulomb Gas

The thermodynamic problem of a gas of static quarks carrying U(N) charges and interacting with each other via U(N) electric gauge fields is formulated and solved in the large N limit. In a lattice theory, the solution can be found in any dimension. In particular, in 1+1-dimensions, the continuum model can also be solved. In that case, and when the quarks are in the adjoint representation, the explicit solution exhibits a first order quark confinement-deconfinement transition at a critical temperature and density. We also show that, when there are fundamental representation quarks, this phase transition persists until the relative density of fundamental quarks is comparable to the density of adjoint quarks, where it becomes a third order transition. We discuss the possible interpretation of the third order transition as deconfinement.

hep-ph↗

arXiv1998

Spectrum of the 2-Flavor Schwinger Model from the Heisenberg Spin Chain

We study the strong coupling limit of the 2-flavor lattice Schwinger model in the Hamiltonian formalism using staggered fermions. We show that the problem of finding the low-lying states is equivalent to solving the Heisenberg antiferromagnetic spin chain. We find good agreement with the continuum theory.

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arXiv1998

Phase transition induced by a magnetic field

The magnetic catalysis of discrete chiral symmetry breaking in the 2+1 dimensional Nambu-Jona-Lasinio model is analyzed. A particular attention is paid to a possible application of the effect in solid state physics. The fermion contribution to the thermal conductivity as a function of the dynamical mass (energy gap in the spectrum) is estimated and is shown to be suppressed when a non-zero order parameter develops.

hep-ph↗

arXiv1998

Topology and Duality in Abelian Lattice Theories

We show how to obtain the dual of any lattice model with inhomogeneous local interactions based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains disorder loops on the generators of the cohomology group of a particular dimension. An explicit construction for altering the statistical sum to obtain a self-dual theory, when these obstructions exist, is also given. We discuss some applications of these results, particularly the existence of non-trivial self-dual 2-dimensional Z_N theories on the torus. In addition we explicitly construct the n-point functions of plaquette variables for the U(1) gauge theory on the 2-dimensional g-tori.

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arXiv1998

Loops, Surfaces and Grassmann Representation in Two- and Three-Dimensional Ising Models

Starting from the known representation of the partition function of the 2- and 3-D Ising models as an integral over Grassmann variables, we perform a hopping expansion of the corresponding Pfaffian. We show that this expansion is an exact, algebraic representation of the loop- and surface expansions (with intrinsic geometry) of the 2- and 3-D Ising models. Such an algebraic calculus is much simpler to deal with than working with the geometrical objects. For the 2-D case we show that the algebra of hopping generators allows a simple algebraic treatment of the geometry factors and counting problems, and as a result we obtain the corrected loop expansion of the free energy. We compute the radius of convergence of this expansion and show that it is determined by the critical temperature. In 3-D the hopping expansion leads to the surface representation of the Ising model in terms of surfaces with intrinsic geometry. Based on a representation of the 3-D model as a product of 2-D models coupled to an auxiliary field, we give a simple derivation of the geometry factor which prevents overcounting of surfaces and provide a classification of possible sets of surfaces to be summed over. For 2- and 3-D we derive a compact formula for 2n-point functions in loop (surface) representation.

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arXiv1997

Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled Lattice Schwinger Model

We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. We show that this discrete symmetry is indeed broken spontaneously in the strong coupling li mit. Expanding around a gauge invariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong coupling expansion and compute the masses of the low lying bosonic excitations as well as the chiral co ndensate of the model. We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong coupling perturbation theory. We also find the exact ground state of the antiferromag netic Ising spin chain with long range Coulomb interaction, which determines the nature of the ground state in the strong coupling limit.

hep-lat↗

arXiv1997

The Mixed Non-Abelian Coulomb Gas in Two Dimensions

The statistical mechanics of a mixed gas of adjoint and fundamental representation charges interacting via 1+1-dimensional U(N) gauge fields is investigated. In the limit of large N we show that there is a first order deconfining phase transition for low densities of fundamental charges. As the density of fundamental charges becomes comparable to the adjoint charge density the phase transition becomes a third order one.

hep-th↗

arXiv1997

Loop Correlators and Theta States in 2D Yang-Mills Theory

Explicit computations of the partition function and correlation functions of Wilson and Polyakov loop operators in theta-sectors of two dimensional Yang-Mills theory on the line cylinder and torus are presented. Several observations about the correspondence of two dimensional Yang-Mills theory with unitary matrix quantum mechanics are presented. The incorporation of the theta-angle which characterizes the states of two dimensional adjoint QCD is discussed.

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