We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of this subject.
No abstract is provided for this article.
Magnetic susceptibility (1.45–300 K), zero and high field Mössbauer spectroscopy, IR and solution conductivity measurements were used to characterize the title DMR adduct, Fe(phen)Cl3·DMF. The absence of magnetic hyperfine splitting in zero external field is correlated with D positive corresponding to an isolated, rapidly relaxing ground (M s = ± 1 2 Kramers doublet. X-ray data show that the ferric ion centres are apparently sufficiently close (∼ 7 Å) to allow for rapid spin-spin relaxation via dipolar interactions. The application of longitudinal magnetic fields (0–5 Tesla for 1.7–4.2 K) slows relaxation and results in fully resolved Zeeman split Mössbauer spectra for which the effective internal field, H n = 354 kG at 1.7 K for H 0 = 5T. The complex [Fe(phen)3] [O(FeCl3)2] contains an unusual binuclear anion based on tetrahedral FeOCl3 units as recently found in [pyridinium]2[O(FeCl3)2] and is obtained as a trace by-product in our preparation of Fe(phen)Cl3·DMF. Further magnetic characterization of the latter pyridinium compound is presented.
Let M be a complete Einstein manifold of negative curvature, and assume that (as in the AdS/CFT correspondence) it has a Penrose compactification with a conformal boundary TV of positive scalar curvature.We show that under these conditions, jy n (M;Z) = 0 and in particular N must be connected.These results resolve some puzzles concerning the AdS/CFT correspondence.
In this chapter we discuss one-loop amplitudes in superstring theory. The operator methods used for the calculations of one-loop amplitudes with on-shell external states in chapter 8 will be applied to the calculation of the corresponding diagrams in superstring theories. The resulting amplitudes are expressed as integrals over world sheets that are closed and orientable in the case of the type II or heterotic theories. Type I theories are based on unoriented open and closed strings, and as a result their world sheets need not be orientable and can have boundaries. As in the case of the bosonic theory, the operator approach automatically gives the correct measure factors by elementary algebraic manipulations. In approaches that explicitly compute the sum over geometries, considerable care is required to correctly define and evaluate infinite determinants that give the measure. Nonetheless, such approaches have a number of advantages and certainly appear preferable for the study of multiloop amplitudes.
This note aims to provide an entr\'ee to two developments in two-dimensional topological gravity -- that is, intersection theory on the moduli space of Riemann surfaces -- that have not yet become well-known among physicists. A little over a decade ago, Mirzakhani discovered \cite{M1,M2} an elegant new proof of the formulas that result from the relationship between topological gravity and matrix models of two-dimensional gravity. Here we will give a very partial introduction to that work, which hopefully will also serve as a modest tribute to the memory of a brilliant mathematical pioneer. More recently, Pandharipande, Solomon, and Tessler \cite{PST} (with further developments in \cite{Tes,BT,STa}) generalized intersection theory on moduli space to the case of Riemann surfaces with boundary, leading to generalizations of the familiar KdV and Virasoro formulas. Though the existence of such a generalization appears natural from the matrix model viewpoint -- it corresponds to adding vector degrees of freedom to the matrix model -- constructing this generalization is not straightforward. We will give some idea of the unexpected way that the difficulties were resolved.
We present a conformal field theory which desribes a homogeneous four dimensional Lorentz-signature space-time. The model is an ungauged WZW model based on a central extension of the Poincar\'e algebra. The central charge of this theory is exactly four, just like four dimensional Minkowski space. The model can be interpreted as a four dimensional monochromatic plane wave. As there are three commuting isometries, other interesting geometries are expected to emerge via $O(3,3)$ duality.
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.
The purpose of this article is to describe some themes in theoretical physics that developed independently for many years, in some cases for decades, and then converged rather suddenly beginning around 1994–95. The convergence produced an upheaval sometimes called “the second superstring revolution.” It is as significant in its own way as “the first superstring revolution,” the period around 1984–85 when the potential of string theory to give a unified description of natural law was first widely appreciated.
The physical degrees of freedom of free actions involving antisymmetric tensor fields are analyzed. While massless spin zero as well as massive vector particles can be represented by such fields, we show that massive scalars cannot, and that some actions have no dynamical content at all. We also show that electromagnetic (unlike gravitational) interactions cannot be included consistently in the spin zero case. Supersymmetric extension of the tensor formulation is given, and it is shown that, in analogous antisymmetric tensor-spinor incarnations, fermions cannot couple consistently to gravity.
We propose an algebra of operators along an observer's worldline as a background-independent algebra in quantum gravity. In that context, it is natural to think of the Hartle-Hawking no boundary state as a universal state of maximum entropy, and to define entropy in terms of the relative entropy with this state. In the case that the only spacetimes considered correspond to de Sitter vacua with different values of the cosmological constant, this definition leads to sensible results.
No abstract is provided for this article.
The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities, Stokes phenomena, isomonodromic deformation, and, from a physical point of view, new surface operators associated with higher order singularities.
General conditions for dynamical supersymmetry breaking are discussed. Very small effects that would usually be ignored, such as instantons of a grand unified theory, might break supersymmetry at a low energy scale. Examples are given (in 0 + 1 and 2 + 1 dimensions) in which dynamical supersymmetry breaking occurs. Difficulties that confront such a program in four dimensions are described.
Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting $SU(2)$ instantons, one can define equivalent four-manifold invariants by counting solutions of a non-linear equation with an abelian gauge group. This is a ``dual'' equation in which the gauge group is the dual of the maximal torus of $SU(2)$. The new viewpoint suggests many new results about the Donaldson invariants.
We explore the dynamics of a simple class of two-dimensional models with $(0,1)$ supersymmetry, namely sigma-models with target $S^3$ and the minimal possible set of fields. For any nonzero value of the Wess--Zumino coupling $k$, we describe a superconformal fixed point to which we conjecture that the model flows in the infrared. For $k=0$, we conjecture that the model spontaneously breaks supersymmetry. We further explore the question of whether this model can be continuously connected to one that spontaneously breaks supersymmetry by "flowing up and down the renormalization group trajectories," in a sense that we describe. We show that this is possible if $k$ is a multiple of 24, or equivalently if the target space with its $B$-field is the boundary of a "string manifold." The mathematical theory of "topological modular forms" suggests that this condition is necessary as well as sufficient.
