115179854
Orientifold Precis
We give a precise and concise formulation of the orientifold construction in Type II superstring theory. Our results include anomaly cancellation on the worldsheet and a K-theoretic computation of the background Ramond-Ramond charge. Since its inception [Sa, PS, Ho, DLP, BiS] the orientifold construction of Type II superstring theory has proven useful both for the formal development of string theory and for its potential applications to phenomenology. For reviews see [P, D, AnS, BH1, J, BH2, BHHW]. Our work began many years ago when the first author showed the second the formula [DJM, CR, MSS, S, SS] for the Ramond-Ramond charge induced by an orientifold and inquired about its K-theoretic significance, especially in view of the unusual cousin of the Hirzebruch L-genus contained therein. In the process of our investigations we were led to more foundational questions about orientifolds and the Type II superstring. In this letter we describe some mathematical foundations we have developed to resolve these questions. In particular, we give careful definitions of both the worldsheet and spacetime fields of an orientifold, including precise Dirac quantization conditions for the B-field and Ramond-Ramond (RR) field. The pNeveu-Schwarzq2 NSNS fields which appear in Definition 2 involve subtle topological structures which, for very different reasons, exactly fit what is needed in both the (short distance) worldsheet and (long distance) spacetime theories. The worldsheet fields are enumerated in Definition 4. A surprising challenge here is to define the integral of the B-field over the worldsheet. The lack of a proper orientation leads to a novel prescription, one feature of which is that the B-field amplitude has a (classical) anomaly in the sense that it takes values in a complex line not canonically isomorphic to the complex numbers. It then cancels against the more standard (quantum) anomaly from the spinor field on the worldsheet, and the cancellation uses the “twisted” spin structure in spacetime. The spacetime RR field is self-dual, so part of its formulation (Definition 6) involves a certain quadratic function. The general theory of self-dual fields defines an RR charge due to the orientifold background, which we compute with the prime 2 inverted, in which case it localizes to the orientifold fixed point set. Tensoring with the reals we recover the formula (8) which began this project. Our definitions are new, even in the case of the Type I superstring, and offer some refinements of the standard (non-orientifold) Type II superstring. Taken together the orientifold data is an impressively tight structure, and leads to the most intricate matching we know between topological Date: August 19, 2010. The work of J.D. is supported by the National Science Foundation under grant PHY-0455649. The work of D.S.F. is supported by the National Science Foundation under grant DMS-0603964. The work of G.W.M. is supported by the DOE under grant DE-FG02-96ER40949. We also thank the Aspen Center for Physics for providing a stimulating environment for many discussions related to this paper. Report numbers: UTTG-04-09, TCC-019-09. The twisted spin structure appears in Definition 2.
118337669
Symmetries of the Bosonic String S-Matrix
The bracket operation on mutually local BRST classes may be combined with Lorentz invariance and analyticity to write an infinite set of finite difference relations on string scattering amplitudes. When combined with some simple physical criteria these relations uniquely determine the genus zero string $S$-matrix for $N\leq 26$-particle scattering in $\IR^{25,1}$ in terms of a single parameter, $\kappa$, the string coupling. We propose that the high-energy limit of the relations are the Ward identities for the high-energy symmetries of string theory.
124306496
The M theory three form and E(8) gauge theory
122595912
Anomalies in Nonlinear $\sigma$ Models
Certain nonlinear sigma models with fermions suffer from an anomaly similar to the one in non-Abelian gauge theory. We exhibit this anomaly using both perturbative and global methods. The affected theories are ill defined and hence unsuitable for describing low-energy dynamics. They include certain supersymmetric models in four space-time dimensions.
15868022
Donaldson Invariants for Non-Simply Connected Manifolds
Abstract:We study Coulomb branch (“u-plane”) integrals for supersymmetric SU(2),SO(3) Yang–Mills theory on 4-manifolds X of b1(X)>0, b2+(X)= 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b1(X)>0, b2+(X)>0. Explicit expressions for , where Fg is a Riemann surface of genus g are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.
14205277
Melvin Models and Diophantine Approximation
Melvin models with irrational twist parameter provide an interesting example of conformal field theories with non-compact target space, and localized states which are arbitrarily close to being delocalized. We study the torus partition sum of these models, focusing on the properties of the regularized dimension of the space of localized states. We show that its behavior is related to interesting arithmetic properties of the twist parameter γ, such as the Lyapunov exponent. Moreover, for γ in a set of measure one the regularized dimension is in fact not a well-defined number but must be considered as a random variable in a probability distribution.
12239452
Lower bound on the propagation speed of gravity from gravitational Cherenkov radiation
Recently, interesting 4-D Lorentz violating models have been proposed, in which all particles have a common maximum velocity c, but gravity propagates (in the preferred frame) with a different maximum velocity cg≠c. We show that the case cg < c is very tightly constrained by the observation of the highest energy cosmic rays. Assuming a galactic origin for the cosmic rays gives a conservative bound of c−cg <2 × 10−15c; if the cosmic rays have an extragalactic origin the bound is orders of magnitude tighter, of order c−cg < 2 × 10−19c.
119468202
The nonperturbative broken phase sphaleron rate
Abstract I present a technique for measuring the broken phase sphaleron rate nonperturbatively. There are three parts to the calculation: determination of the probability distribution of Chern-Simons number N CS ; measurement of 〈| dN CS / dt |〉 N CS = 1 2 , the mean rate of change of N CS at the barrier; and measurement of the “dynamical prefactor,” the fraction of barrier crossings which result in a permanent integer change in N CS .
10799212
Classical field dynamics of the electroweak phase transition
We investigate the thermodynamics and dynamics of the electroweak phase transition by modeling the infrared physics with classical Yang-Mills Higgs theory. We discuss the accuracy of this approach and conclude that, for quantities whose determination is dominated by the infrared, the classical method should be correct up to parametrically suppressed [i.e., O({alpha})] corrections. For a Higgs self-coupling which at the tree level corresponds to m{sub H}{approx_equal}50 GeV, we determine the jump in the order parameter to be {delta}{phi}=1.5gT, the surface tension to be {sigma}=0.07g{sup 4}T{sup 3}, and the friction coefficient on the moving bubble wall due to infrared bosons to be {eta}{equivalent_to}P/v{sub w}=0.03{plus_minus}0.004g{sup 6}T{sup 4}. We also investigate the response of the Chern-Simons number to a spatially uniform chemical potential and find that it falls off a short distance inside the bubble wall, both in equilibrium and below the equilibrium temperature. {copyright} {ital 1997} {ital The American Physical Society}
118805589
Second order hydrodynamic coefficients from kinetic theory
In a relativistic setting, hydrodynamic calculations which include shear viscosity (which is first order in an expansion in gradients of the flow velocity) are unstable and acausal unless they also include terms to second order in gradients. To date such terms have only been computed in supersymmetric N=4 super-Yang-Mills theory at infinite coupling. Here we compute these second-order hydrodynamic coefficients in weakly coupled QCD, perturbatively to leading order in the QCD coupling, using kinetic theory. We also compute them in QED and scalar {lambda}{phi}{sup 4} theory.
12818530
Electroweak bubble nucleation, nonperturbatively
We present a lattice method to compute bubble nucleation rates at radiatively induced first order phase transitions, in high temperature, weakly coupled field theories, nonperturbatively. A generalization of Langer's approach, it makes no recourse to saddle point expansions and includes completely the dynamical prefactor. We test the technique by applying it to the electroweak phase transition in the minimal standard model, at an unphysically small Higgs mass which gives a reasonably strong phase transition (lambda/g^2 =0.036, which corresponds to m(Higgs)/m(W) = 0.54 at tree level but does not correspond to a positive physical Higgs mass when radiative effects of the top quark are included), and compare the results to older perturbative and other estimates. While two loop perturbation theory slightly under-estimates the strength of the transition measured by the latent heat, it over-estimates the amount of supercooling by a factor of 2.