12568136
Correlations and renormalization in lattice gases.
An exact kinetic theory is formulated for lattice gases. This kinetic theory makes possible the calculation of corrections to the usual combined Boltzmann and Chapman-Enskog analysis of lattice gases due to the buildup of correlations. Cluster expansion methods are used to show that renormalized transport coefficients for lattice gases satisfying semidetailed balance can be calculated perturbatively by summing terms in an infinite series. A diagrammatic notation for the terms in this series is given, in analogy with the diagrammatic expansions of continuum kinetic theory and quantum field theory. A closed-form expression for the coefficients associated with the vertices of these diagrams is given. This method is applied to several standard lattice gases, and the results are shown to correctly predict observed deviations from the Boltzmann analysis.
17735606
FLUCTUATION SPECTRA OF TILTED AND INTERSECTING D-BRANES FROM THE BORN-INFELD ACTION
Abstract We consider the spectra of excitations around diagonal and intersecting D-brane configurations on tori. These configurations are described by constant curvature connections in a dual gauge theory description. The low-energy string fluctuation spectrum is reproduced exactly by the gauge theory in the case of vanishing field strength; however, this correspondence breaks down for fixed non-zero field strength. We show that in many cases the full Born-Infeld action correctly captures the low-energy spectrum in the case of non-vanishing field strength. This gives a field theory description of the low-energy physics of systems of diagonally wound branes and branes at angles as considered by Berkooz, Douglas and Leigh. This description extends naturally to non-supersymmetric configurations, where the tachyonic instability associated with brane-antibrane systems appears as an instability around a saddle point solution of the corresponding Yang-Mills/Born-Infeld theory. In some cases, the field theory description requires a non-abelian generalization of the Born-Infeld action. We follow Tseytlin's recent proposal for formulating such an action. In the case of intersecting branes, the non-abelian Bom-Infeld theory produces a transcendental relation which comes tantalizingly close to reproducing the correct spectrum; however, a discrepancy remains which indicates that a further clarification of the non-abelian Born-Infeld action may be necessary.
12152062
The landscape of intersecting brane models
We develop tools for analyzing the space of intersecting brane models. We apply these tools to a particular T6/22 orientifold which has been used for model building. We prove that there are a finite number of intersecting brane models on this orientifold which satisfy the Diophantine equations coming from supersymmetry. We give estimates for numbers of models with specific gauge groups, which we confirm numerically. We analyze the distributions and correlations of intersection numbers which characterize the numbers of generations of chiral fermions, and show that intersection numbers are roughly independent, with a characteristic distribution which is peaked around 0 and in which integers with fewer divisors are mildly suppressed. As an application, the number of models containing a gauge group SU(3) × SU(2) × U(1) or SU(4) × SU(2) × SU(2) and 3 generations of appropriate types of chiral matter is estimated to be order (10), in accord with previous explicit constructions. As another application of the methods developed in the paper, we construct a new pair of 3-generation SU(4) × SU(2) × SU(2) Pati-Salam models using intersecting branes. We conclude with a description of how this analysis can be generalized to a broader class of Calabi-Yau orientifolds, and a discussion of how the numbers of IBM's are related to numbers of stabilized vacua.
119451798
D-brane effective field theory from string field theory
Abstract Open string field theory is considered as a tool for deriving the effective action for the massless or tachyonic fields living on D-branes. Some simple calculations are performed in open bosonic string field theory which validate this approach. The level truncation method is used to calculate successive approximations to the quartic terms φ 4 , (A μ A μ ) 2 and [A μ ,A ν ] 2 for the zero momentum tachyon and gauge field on one or many bosonic D-branes. We find that the level truncation method converges for these terms within 2–4% when all massive fields up to level 20 are integrated out, although the convergence is slower than exponential. We discuss the possibility of extending this work to determine the structure of the nonabelian Born–Infeld theory describing the gauge field on a system of many parallel bosonic or supersymmetric D-branes. We also describe a brane configuration in which tachyon condensation arises in both the gauge theory and string field theory pictures. This provides a natural connection between recent work of Sen and Zwiebach on tachyon condensation in string field theory and unstable vacua in super Yang–Mills and Born–Infeld field theory.
11357594
Inflationary Constraints on Type IIA String Theory
We prove that inflation is forbidden in the most well understood class of semi-realistic type IIA string compactifications: Calabi-Yau compactifications with only standard NS-NS 3-form flux, R-R fluxes, D6-branes and O6-planes at large volume and small string coupling. With these ingredients, the first slow-roll parameter satisfies epsilon >= 27/13 whenever V > 0, ruling out both inflation (including brane/anti-brane inflation) and de Sitter vacua in this limit. Our proof is based on the dependence of the 4-dimensional potential on the volume and dilaton moduli in the presence of fluxes and branes. We also describe broader classes of IIA models which may include cosmologies with inflation and/or de Sitter vacua. The inclusion of extra ingredients, such as NS 5-branes and geometric or non-geometric NS-NS fluxes, evades the assumptions used in deriving the no-go theorem. We focus on NS 5-branes and outline how such ingredients may prove fruitful for cosmology, but we do not provide an explicit model. We contrast the results of our IIA analysis with the rather different situation in IIB.
117081961
Counting Strings and Phase Transitions in 2D QCD
Several string theories related to QCD in two dimensions are studied. For each of these theories the large $N$ free energy on a (target) sphere of area $A$ is calculated. By considering theories with different subsets of the geometrical structures involved in the full QCD${}_2$ string theory, the different contributions of these structures to the string free energy are calculated using both analytic and numerical methods. The equivalence between the leading terms in the $SU(N)$ and $U(N)$ free energies is simply demonstrated from the string formulation. It is shown that when $\Omega$-points are removed from the theory, the free energy is convergent for small and large values of $A$ but divergent in an intermediate range. Numerical results indicate that the free energy for the full QCD${}_2$ string fails to converge at the Douglas-Kazakov phase transition point. Similar results for a single chiral sector of the theory, such as has recently been studied by Cordes, Moore, and Ramgoolam, indicate that there are three distinct phases in that theory. These results indicate that from the point of view of the strong coupling phase, the phase transition in the full QCD${}_2$ string arises from the entropy of branch-point singularities.
33049133
Vacuum structure, zero modes, and the effective potential in light-cone quantization.
A Hamiltonian formalism for the calculation of the usual effective potential is presented in the context of scalar field theory. When applied in the context of light-cone quantization, we find contributions at [ital k][sup +]=0 which are missed by standard light-cone infrared regularizations. We present a (time-dependent) regularization of the Hamiltonian which correctly incorporates these contributions at the one-loop level. We briefly discuss the implications of these findings for the more general program of diagonalizing the light-cone Hamiltonian.
38327098
Quantizing compact phase spaces: Irreducible representations from constrained dynamics.
We study the quantization of the coset space SU(3)/U(1){times}U(1), considered as an example of a compact phase space. We embed this system in the flat space {ital C}{sup 6} endowed with a Poisson-bracket structure, then quantize it as a constrained system, finding consistency only for isolated symplectic structures. The space of states for each admissible symplectic structure forms an irreducible representation of SU(3). In this way, we recover in the language of constrained dynamics some of the results of the Borel-Weil-Bott theorem and geometric quantization.
17862595
Role of zero modes in the canonical quantization of heavy-fermion QED in light-cone coordinates.
Four-dimensional heavy-fermion QED is studied in light-cone coordinates with (anti)periodic field boundary conditions. We carry out a consistent light-cone canonical quantization of this model using the Dirac algorithm for a system with first- and second-class constraints. To examine the role of the zero modes, we consider the quantization procedure in the zero mode and the nonzero-mode sectors separately. In both sectors we obtain the physical variables and their canonical commutation relations. The physical Hamiltonian is constructed via a step-by-step exclusion of the unphysical degrees of freedom. An example using this Hamiltonian in which the zero modes play a role is the verification of the correct Coulomb potential between two heavy fermions.