802 publications from this institution
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.
In bosonic JT gravity, minimally coupled to bulk matter, there exists a single, delta-function-normalisable state in each $SL(2,R)$ representation of the matter QFT for any pair of positive energies $E_L, E_R$ at the left and right boundaries. In $\mathcal{N} = 2$ super-JT gravity coupled to matter, we show that there exists a single normalisable state in each $SU(1,1|1)$ matter representation (given appropriate R-charges) that has exactly zero energy at both boundaries. For non-BPS representations, these states have the peculiar property that they break all supersymmetry in the bulk, while preserving supersymmetry at both boundaries. Projecting the algebras of boundary observables onto these zero-energy states leads to a Type II$_1$ von Neumann factor at each boundary that contains a single operator for each supersymmetric matter boundary primary with sufficiently small R-charge. For neutral boundary primaries, the Type II$_1$ factor has a natural action on the matter QFT Hilbert space (with no additional gravitational degrees of freedom) such that the QFT vacuum is the unique tracial state. Moreover, the product of neutral matter operators can be found very explicitly and has a remarkably simple form. When primaries with nonzero matter R-charge are included, the trace can be written as a sum over matter vacuum expectation values associated to each allowed boundary R-charge $J_R$, with the terms in the sum weighted by $\mathrm{cos}(\pi J_R)$. In this way, the ground state algebras encode the ratios of the number of BPS microstates within each R-charge sector. In addition to the results on super-JT gravity described above, we provide a purely Lorentzian derivation of the algebraic structure of canonically quantised (bosonic) JT gravity plus matter, without appeal to the Euclidean gravitational path integrals used in previous work.
An exact conformal field theory describing a black hole in two-dimensional space-time is found as an SL(2,openR)/U(1) gauged Wess-Zumino-Witten model. For k=9/4, the conformal field theory can be regarded as a classical solution of the same system that is probed in the c=1 matrix model. The conformal field theory governing the space-time is regular at the Riemannian singularity, but it appears that generic perturbations blow up there. It is argued that the end point of the Hawking black-hole evaporation is the standard space-time of the c=1 matrix model, which should be regarded as an analog of the extreme Reissner-Nordstr\"om black hole of four-dimensional general relativity. The c=1 model is thus a model of the quantum mechanics of matter interacting with a black hole.
In these lecture notes from Strings `91, I briefly sketch the analogy between two dimensional black holes and the s-wave sector of four dimensional black holes, and the physical interest of the latter, particularly in the magnetically charged case.
We review what is known about boundary conditions in General Relativity on a spacetime of Euclidean signature. The obvious Dirichlet boundary condition, in which one specifies the boundary geometry, is actually not elliptic and in general does not lead to a well-defined perturbation theory. It is better-behaved if the extrinsic curvature of the boundary is suitably constrained, for instance if it is positive- or negative-definite. A different boundary condition, in which one specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and always leads formally to a satisfactory perturbation theory. These facts might have interesting implications for semiclassical approaches to quantum gravity. April, 2018
New instanton effects in supersymmetric QCD, Chris Beasley, Edward Witten
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The canonical quantization of Chern-Simons gauge theory in 2+1 dimensions is generalized from the case in which the gauge group is a compact Lie groupG to
We generalize the half-BPS Janus configuration of four-dimensional $ \mathcal{N} = 4 $ super Yang-Mills theory to allow the theta-angle, as well as the gau
A first-order QCD phase transition that occurred reversibly in the early universe would lead to a surprisingly rich cosmological scenario. Although observable consequences would not necessarily survive, it is at least conceivable that the phase transition would concentrate most of the quark excess in dense, invisible quark nuggets, providing an explanation for the dark matter in terms of QCD effects only. This possibility is viable only if quark matter has energy per baryon less than 938 MeV. Two related issues are considered in appendices: the possibility that neutron stars generate a quark-matter component of cosmic rays, and the possibility that the QCD phase transition may have produced a detectable gravitational signal.
The mystery of the cosmological constant is probably the most pressing obstacle to significantly improving the models of elementary particle physics derived from string theory. The problem arises because in the standard framework of low energy physics, there appears to be no natural explanation for vanishing or extreme smallness of the vacuum energy, while on the other hand it is very difficult to modify this framework in a sensible way. In seeking to resolve this problem, one naturally wonders if the real world can somehow be interpreted in terms of a vacuum state with unbroken supersymmetry.
The consequences for cosmology of a Coleman-E. Weinberg light Higgs boson are considered. If SU(2) × U(1) symmetry breaking is induced by such a boson, the early universe went far out of equilibrium at the time of the SU(2) × U(1) phase transition. The universe supercooled far below the equilibrium transition temperature. The decay of the unstable vacuum, when it finally occured, was induced by a process of “dynamical symmetry breaking” and increased the entropy to baryon ratio of the universe by a factor of 105 or 106. (Related matters have been treated in recent work by Guth and E. Weinberg.)
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In this paper the existing results concerning mesons and glue states in the large-N limit of QCD are reviewed, and it is shown how to fit baryons into this picture.
We construct a Type II$_\infty$ von Neumann algebra that describes the large $N$ physics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative $1/N$ corrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the QES prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in the $G \to 0$ limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the generalized second law is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a "free product" von Neumann algebra that describes the semiclassical physics of long wormholes supported by shocks. We compute Rényi entropies for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to "bulge" quantum extremal surfaces contribute with a negative sign.
Einstein's breakthroughs in 1905 have been celebrated at conferences around the world, with more planned for later this year. However, few of these events have been in the Islamic or developing world,which is why a major Einstein celebration in a leading Islamic country like Egypt is a significant event.
