14355358
Comments on heterotic flux compactifications
In heterotic flux compactification with supersymmetry, three different connections with torsion appear naturally, all in the form ω+aH. Supersymmetry condition carries a = −1, the Dirac operator has a = −1/3, and higher order term in the effective action involves a = 1. With a view toward the gauge sector, we explore the geometry with such torsions. After reviewing the supersymmetry constraints and finding a relation between the scalar curvature and the flux, we derive the squared form of the zero mode equations for gauge fermions. With dH = 0, the operator has a positive potential term, and the mass of the unbroken gauge sector appears formally positive definite. However, this apparent contradiction is avoided by a no-go theorem that the compactification with H≠0 and dH = 0 is necessarily singular, and the formal positivity is invalid. With dH≠0, smooth compactification becomes possible. We show that, at least near smooth supersymmetric solution, the size of H2 should be comparable to that of dH and the consistent truncation of the action has to keep α'R2 term. A warp factor equation of motion is rewritten with α'R2 contribution included precisely, and some limits are considered.
8177695
Gauged linear sigma models for noncompact Calabi-Yau varieties
Abstract We study gauged linear sigma models for noncompact Calabi–Yau manifolds described as a line bundle on a hypersurface in a projective space. This gauge theory has a unique phase if the Fayet–Iliopoulos parameter is positive, while there exist two distinct phases if the parameter is negative. We find four massless effective theories in the infrared limit, which are related to each other under the Calabi–Yau/Landau–Ginzburg correspondence and the topology change. In the T-dual theory, on the other hand, we obtain two types of exact massless effective theories: one is the sigma model on a newly obtained Calabi–Yau geometry as a mirror dual, while the other is given by a Landau–Ginzburg theory with a negative power term, indicating N = 2 superconformal field theory on SL ( 2 , R ) / U ( 1 ) . We argue that the effective theories in the original gauged linear sigma model are exactly realized as N = 2 Liouville theories coupled to well-defined Landau–Ginzburg minimal models.
651290
A note on conifolds
Abstract We present the Ricci-flat metric and its Kahler potential on the conifold with the O ( N ) isometry, whose conical singularity is repaired by the complex quadric surface Q N −2 = SO ( N )/ SO ( N −2)× U (1).
119194039
Canonical approach to Courant brackets for D-branes
A bstractWe present an extension of the Courant bracket to the ones for Dp-branes by analyzing Hamiltonians and local superalgebras. Contrast to the basis of the bracket for a fundamental string which consists of the momentum and the winding modes, the ones for Dp-branes contain higher rank R-R coupling tensors. We show that the R-R gauge transformation rules are obtained by these Courant brackets for Dp-branes where the Dirac-Born-Infeld gauge field and the “two-vierbein field” play an essential role. Canonical analysis of the worldvolume theories naturally gives the basis of the brackets and the target space backgrounds keeping T-duality manifest at least for NS-NS sector. In a D3-brane analysis S-duality is manifest as a symmetry of interchanging the NS-NS coupling and the R-R coupling.
118872049
Worldsheet description of exotic five-brane with two gauged isometries
A bstractWe study the string worldsheet description of the background geometry of the exotic $ 5_2^2 $-brane where two isometries are gauged. This is an extension of the gauged linear sigma model (GLSM) for the exotic $ 5_2^2 $-brane with a single gauged isometry. The new GLSM with two gauged isometries has only $ \mathcal{N} $ = (2, 2) supersymmetry rather than $ \mathcal{N} $ = (4, 4) supersymmetry of the original GLSM. This is caused by a conflict between two different SU(2)R associated with the two gauge symmetries. However, if we take a certain limit, we can find the genuine string sigma model of the background geometry of the exotic $ 5_2^2 $-brane with $ \mathcal{N} $ = (4, 4) supersymmetry. We also investigate the worldsheet instanton corrections to the background geometry of the exotic $ 5_2^2 $-brane. The worldsheet instanton corrections to the string sigma model can be traced in terms of the two gauge fields in the new GLSM. This new GLSM gives rise to a different feature of the quantum corrections from the one in the GLSM with the single gauged isometry.
15429929
Supersymmetric nonlinear sigma models on Ricci-flat Kähler manifolds with O(N) symmetry
Abstract We propose a class of N =2 supersymmetric nonlinear sigma models on the Ricci-flat Kahler manifolds with O( N ) symmetry.
118151125
Gauge Theory, Combinatorics, and Matrix Models
Quantum field theory is the most universal method in physics, applied to all the area from condensed-matter physics to high-energy physics. The standard tool to deal with quantum field theory is the perturbation method, which is quite useful if we know the vacuum of the system, namely the starting point of our analysis. On the other hand, sometimes the vacuum itself is not obvious due to the quantum nature of the system. In that case, since the pertur‐ bative method is not available any longer, we have to treat the theory in a non-perturbative way.
126022579
Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions
We present a theoretical foundation for the index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology and the number of species doublers. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms.
118426022
The Chiral Heat Effect
(Received January 3, 2012; Revised May 1, 2012)We consider the thermal response of a (3+1)-dimensional theory with a chiral anomalyonacurved space motivatedbythechiralmagneticeﬀect. Weﬁnd anew phenomenon, calledthe chiral heat eﬀect, such that the thermal current is induced transverse to a gradient ofthe temperature even on a ﬂat space. We study a similar topological eﬀect on the spacetimewith a torsion.
15996221
Aoki phases in the lattice Gross-Neveu model with flavored mass terms
We investigate the parity-broken phase structure for staggered and naive fermions in the Gross-Neveu model as a toy model of QCD. We consider a generalized staggered Gross-Neveu model including two types of four-point interactions. We use generalized mass terms to split the doublers for both staggered and naive fermions. The phase boundaries derived from the gap equations show that the mass splitting of tastes results in an Aoki phase both in the staggered and naive cases. We also discuss the continuum limit of these models and explore taking the chirally symmetric limit by fine-tuning a mass parameter and two-coupling constants. This supports the idea that in lattice QCD we can derive one- or two-flavor staggered fermions by tuning the mass parameter, which are likely to be less expensive than Wilson fermions in QCD simulation.
55474215
Phase structure of topological insulators by lattice strong-coupling expansion
The effect of the strong electron correlation on the topological phase structure of 2-dimensional (2D) and 3D topological insulators is investigated, in terms of lattice gauge theory. The effective model for noninteracting system is constructed similarly to the lattice fermions with the Wilson term, corresponding to the spin-orbit coupling. Introducing the electron-electron interaction as the coupling to the gauge field, we analyze the behavior of emergent orders by the strong coupling expansion methods. We show that there appears a new phase with the in-plane antiferromagnetic order in the 2D topological insulator, which is similar to the so-called "Aoki phase" in lattice QCD with Wilson fermions. In the 3D case, on the other hand, there does not appear such a new phase, and the electron correlation results in the shift of the phase boundary between the topological phase and the normal phase.