Certain perturbative aspects of two-dimensional sigma models with (0,2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of ``chiral differential operators'' is related to sigma models. In the process, we obtain, for example, an understanding of the one-loop beta function in terms of holomorphic data. A companion paper will study nonperturbative behavior of these theories.
String theory avoids the ultraviolet infinities that arise in trying to quantize gravity. It is also more predictive than conventional quantum field theory, one aspect of this being the way that it contributed to the emergence of the concept of ``supersymmetry'' of particle interactions. There are hints from the successes of supersymmetric unified theories of particle interactions that supersymmetry is relevant to elementary particles at energies close to current accelerator energies; if this is so, it will be confirmed experimentally and supersymmetry is then also likely to be important in cosmology, in connection with dark matter, baryogenesis, and/or inflation. Magnetic monopoles play an important role in the structure of string theory, and thus should certainly exist, if string theory is correct, though they may have been diluted by inflation to an unobservable level. The monopole mass in many attractive models is near the Planck mass, but, if unification of elementary particle forces with gravity occurs near TeV energies through large or warped extra dimensions, as in some recent models, then monopoles should be below 100 TeV and in an astrophysical context would be ultrarelativistic. In such models, supersymmetry would definitely be expected at TeV energies.
I present some exact solutions of the Polyakov-Belavin-Schwartz-Tyupkin equation ${F}_{\ensuremath{\mu}\ensuremath{\nu}}={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{\ensuremath{\mu}\ensuremath{\nu}}$ for an SU(2) gauge theory in Euclidean space. My solutions describe a system with an arbitrary number of pseudoparticles, with arbitrary scale parameters and arbitrary separations, arranged along a line. The action for an $n$-pseudoparticle solution is precisely $n$ times the action for a single pseudoparticle.
No abstract is provided for this article.
The quantization law for the antisymmetric tensor field of M-theory contains a gravitational contribution not known previously. When it is included, the low energy effective action of M-theory, including one-loop and Chern-Simons contributions, is well defined. The relation of M-theory to the E 8 × E 8 heterotic string greatly facilitates the analysis.
Conformal operators for partially massless states
No abstract is provided for this article.
This paper is devoted to the construction of a family of linear sigma models with (0,4) supersymmetry which should flow in the infrared to the stringy version of Yang-Mills instantons on R 4. The family depends on the full set of expected parameters and is obtained by using the data that appear in the ADHM construction of instantons.
The standard boundary state of a topological insulator in 3 + 1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one phase, but also have gapped phases with topological order. Our models are weakly coupled and all the dynamics is explicit. We rederive some known boundary states of topological insulators and construct new ones. Consistency with the standard spin/charge relation of condensed matter physics places a nontrivial constraint on models.
In most field theories that enter physics, the energy is defined as the integral of a gauge invariant physically meaningful energy density T00(x): $$ E = \int {d^3 \times...
We show how some aspects of the K-theory classification of RR fluxes follow from a careful analysis of the phase of the M-theory action. This is a shortened and simplified companion paper to ``E8 Gauge Theory, and a Derivation of K-Theory from M-Theory.''
We analyze the dynamics of M-theory on a manifold of G_2 holonomy that is developing a conical singularity. The known cases involve a cone on CP^3, where we argue that the dynamics involves restoration of a global symmetry, SU(3)/U(1)^2, where we argue that there are phase transitions among three possible branches corresponding to three classical spacetimes, and S^3 x S^3 and its quotients, where we recover and extend previous results about smooth continuations between different spacetimes and relations to four-dimensional gauge theory.
No abstract is provided for this article.
Making use of known facts about "tensor models," it is possible to construct a quantum system without quenched disorder that has the same large $n$ limit for its correlation functions and thermodynamics as the SYK model. This might be useful in further probes of this approach to holographic duality.
No abstract is provided for this article.
The effect of modular transformations which change the spin structure of the string world-sheet is discussed. Invariance of string perturbation theory under such transformations forces us to sum over different spin structures with well defined coefficients. The sum over spin structures amounts to performing the GSO projections. We explain why the GSO projection is compatible with unitarity; that is, why wrong G-parity states are not produced in pairs. On the contrary, we show that unitarity requires either the GSO projection, which gives a supersymmetric spectrum, or another projection which removes the massless spin-3/2 particle from the spectrum. This is in agreement with the familiar idea that a consistent theory with a massless spin-3/2 particle must be supersymmetric. These considerations lead us to find four new string theories in ten dimensions. Although they all have tachyons, they are otherwise consistent, modular invariant and unitary. One of these theories is particularly interesting since it has anomaly free chiral fermions in ten dimensions.
