# Bianchi, Pradisi, Sagnotti ## Toroidal compactification and symmetry breaking in open string theories \[Links: [Inspire](https://inspirehep.net/literature/318848)\] \[Abstract: In toroidal compactification of open-string theories, the background fields of the “parent” closed string (metric and antisymmetric tensor, with suitable restrictions) are accompanied by open-string Wilson lines. In the $SO(32)$ superstring, these control the breaking of the Chan-Paton symmetry in a way that presents interesting analogies with the corresponding phenomenon in the heterotic string. An extension of the closed-string results to include contributions from the disk and the projective plane shows that these fields are genuine “moduli”, since their amplitudes vanish when the momenta are all scaled to zero.\] # Brown, York (a) ## Quasilocal energy and conserved charges derived from the gravitational action \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9209012), [PDF](https://arxiv.org/pdf/gr-qc/9209012.pdf)\] \[Abstract: \] ## Summary - this is the famous Brown-York energy # Brown, York (b) ## The microcanonical functional integral. I. the gravitational field \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9209014), [PDF](https://arxiv.org/pdf/gr-qc/9209014.pdf)\] \[Abstract: \] ## Comments - compared with Noether charge method in [[1995#Iyer, Wald]] # Kontsevich ## Intersection theory on the moduli space of curves and the matrix Airy function \[Links: [Inspire](https://inspirehep.net/literature/342444)\] \[Abstract: We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical problems.\] # Lewellen ## Sewing constraints for conformal field theories on surfaces with boundaries \[Links: [Inspire](https://inspirehep.net/literature/314492), [DOI](https://doi.org/10.1016/0550-3213(92)90370-Q)\] \[Abstract: In a conformal field theory, correlation functions on any Riemann surface are in principle unambiguously defined by sewing together three-point functions on the sphere, provided that the four-point functions on the sphere are crossing symmetric, and the one-point functions on the torus are [[0612 Modular invariance|modular covariant]]. In this work we extend Sonoda's proof of this result to conformal field theories defined on surfaces with boundaries. Four additional [[0602 Moore-Seiberg construction|sewing constraints]] arise; three on the half-plane and one on the cylinder. These relate the various OPE coefficients in the theory (bulk, boundary, and bulk-boundary) to one another. In rational theories these relations can be expressed in terms of data arising solely within the bulk theory: the matrix $S$ which implements modular transformations on the characters, and the matrices implementing duality transformations on the four-point conformal-block functions. As an example we solve these relations for the boundary and bulk-boundary structure constants in the Ising model with all possible conformally invariant boundary conditions. The role of the basic sewing constraints in the construction of open string theories is discussed.\] # Sachdev, Ye ## Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet \[Links: [arXiv](https://arxiv.org/abs/cond-mat/9212030), [PDF](https://arxiv.org/pdf/cond-mat/9212030.pdf)\] \[Abstract: We examine the spin-$S$ quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is accessed by generalizing to $SU(M)$ symmetry and studying the large $M$ limit. For large $S$ the ground state is a spin-glass, while quantum fluctuations produce a spin-fluid state for small $S$. The spin-fluid phase is found to be generically gapless - the average, zero temperature, local dynamic spin-susceptibility obeys $\bar{\chi} (\omega ) \sim \log(1/|\omega|) + i (\pi/2) \mbox{sgn} (\omega)$ at low frequencies. This form is identical to the phenomenological 'marginal' spectrum proposed by Varma *et al.* for the doped cuprates.\] # Sudarsky, Wald ## Extrema of mass, stationarity, and staticity, and solutions to the Einstein Yang-Mills equations \[Links: [Inspire](https://inspirehep.net/literature/342458), [PRD](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.46.1453)\] \[Abstract: A simple formula is derived for the variation of mass and other asymptotic conserved quantities in Einstein-Yang-Mills theory. For asymptotically fiat initial data with a single asymptotic region and no interior boundary, it follows directly from our mass-variation formula that initial data for stationary solutions are extrema of mass at fixed electric charge. When generalized to include an interior boundary, this formula provides a simple derivation of a generalized form of the first law of black-hole mechanics. We also argue, but do not rigorously prove, that in the case of a single asymptotic region with no interior boundary stationarity is necessary for an extremum of mass at fixed charge; when an interior boundary is present, we argue that a necessary condition for an extremum of mass at fixed angular momentum, electric charge, and boundary area is that the solution be a stationary black hole, with the boundary serving as the bifurcation surface of the horizon. Then, by a completely different argument, we prove that if a foliation by maximal slices (i.e. , slices with a vanishing trace of extrinsic curvature) exists, a necessary condition for an extremum of mass when no interior boundary is present is that the solution be static. A generalization of the argument to the case in which an interior boundary is present proves that a necessary condition for a solution of the Einstein-Yang-Mills equation to be an extremum of mass at fixed area of the boundary surface is that the solution be static. This enables us to prove (modulo the existence of a maximal slice) that if the stationary Killing field of a stationary black hole with bifurcate Killing horizon is normal to the horizon, and if the electrostatic potential asymptotically vanishes at infinity, then the black hole must be static. (This closes a significant gap in the black-hole uniqueness theorems. ) Finally, by generalizing the type of argument used to predict the "sphaleron" solution of Yang-Mills-Higgs theory, we argue that the initial-data space for Einstein-Yang-Mills theory with a single asymptotic region should contain a countable infinity of saddle points of mass. Similarly in the case of an interior boundary, there should exist a countable infinity of saddle points of mass at fixed boundary area. We propose that this accounts for the existence and properties of the Bartnik-McKinnon and colored black-hole solutions. Similar arguments in the black-hole case indicate the presence of a countable infinity of extrema of mass at fixed area, electric charge, and angular momentum, thus suggesting the existence of colored generalizations of the charged Kerr solutions. A number of other conjectures concerning stationary solutions of the Einstein-Yang-Mills equations and related systems are formulated. Among these is the prediction of the existence of a countable infinity of new static solutions of the Yang-Mills-Higgs equations related to the sphaleron.\] ## Comments - provides support for the [[0231 Bulk solutions for CFTs on non-trivial geometries|bulk ground state]] being static - uses a Hamiltonian method later employed by [[1993#Jacobson, Myers]] # Turaev, Viro ## State sum invariants of 3 manifolds and quantum 6j symbols \[Links: [Inspire](https://inspirehep.net/literature/332303)\] # Witten (Apr) ## Two Dimensional Gauge Theories Revisited \[Links: [arXiv](https://arxiv.org/abs/hep-th/9204083), [PDF](https://arxiv.org/pdf/hep-th/9204083.pdf)\] \[Abstract: Topological gravity is equivalent to physical gravity in two dimensions in a way that is still mysterious, though by now it has been proved by Kontsevich. In this paper it is shown that a similar relation between topological and physical Yang-Mills theory holds in two dimensions; in this case, however, the relation can be explained by a direct mapping between the two path integrals. This (1) explains many strange facts about [[0618 2d Yang-Mills|two dimensional Yang-Mills]] theory, like the way the partition function can be expressed exactly as a sum over classical solutions, including unstable ones; (2) makes the corresponding topological theory completely computable.\] # Witten (Jul) ## Chern-Simons Gauge Theory As A String Theory \[Links: [arXiv](https://arxiv.org/abs/hep-th/9207094), [PDF](https://arxiv.org/pdf/hep-th/9207094)\] \[Abstract: Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time interpretations. For instance, three-dimensional [[0089 Chern-Simons theory|Chern-Simons gauge theory]] can arise as a string theory. The world-sheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the space-time Chern-Simons theory. A certain holomorphic analog of Chern-Simons theory can also arise as a string theory.\]