16060889
Varieties of vacua in classical supersymmetric gauge theories.
We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the Lagrangian is invariant under the action of the complexified gauge group {ital G}{sup {ital c}}. From this point of view the usual {ital D}-flatness conditions are an artifact of the Wess-Zumino gauge. By using a gauge that preserves {ital G}{sup {ital c}} invariance we show that every constant matter field configuration that extremizes the superpotential is {ital G}{sup {ital c}} gauge equivalent (in a sense that we make precise) to a unique classical vacuum. This result is used to prove that in the absence of a superpotential the classical moduli space is the algebraic variety described by the set of all holomorphic gauge-invariant polynomials. When a superpotential is present, we show that the classical moduli space is a variety defined by imposing additional relations on the holomorphic polynomials. Many of these points are already contained in the existing literature. The main contribution of the present work is that we give a careful and self-contained treatment of limit points and singularities. {copyright} {ital 1996 The American Physical Society.}
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.
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.
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.
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.
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.