The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.
Supersymmetry is a remarkable subject that has fascinated particle physicists since it was originally introduced. Although supersymmetry is no longer a new idea, we still do not know in what form, if any, it plays a role in the proper description of nature.
It is shown that in CP non-conserving theories, the electric charge of an 't Hooft-Polyakov magnetic monopole will not ordinarily be integral, or even rational in units of the fundamental charge e. If a non-zero vacuum angle θ is the only mechanism for CP violation, the electric charge of the monopole is exactly calculable and is −eθ/2π, plus an integer. If there are additional CP violating interactions, the monopole charge must be computed as a power series in the coupling constant. These results apply in realistic theories such as SU(5).
We consider the particle-kink and kink-kink S-matrix elements of the two-dimensional (ψψ)2 model, where the Majorana spinor ψ is an O(N) isovector. Our results confirm many qualitative ideas about the model, including the mass spectrum, the decoupling at N = 4, and the isospinor nature of the kinks.
Some rigorous inequalities governing hadron masses in QCD are proved. One states that the electromagnetic mass shift of the pion is positive. The other states that if ${m}_{A\overline{B}}$ is the mass of the lightest meson made from a quark of type $A$ and an antiquark of type $B$, then---under conditions such that annihilation into gluons can be ignored---$2{m}_{A\overline{B}}>~{m}_{A\overline{A}}+{m}_{B\overline{B}}$. These inequalities agree with experimental data and have analogs for arbitrary vectorlike gauge theories. The first inequality has applications to the vacuum alignment problem in vectorlike technicolor theories.
This lecture surveys a few loosely related topics, ranging from the scarcity of quantum field theories -- and the role that this has played, and still plays, in physics -- to paradoxes involving black holes in soluble two dimensional string theory and the question of whether naked singularities might be of even greater interest to string theorists than black holes.
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.
In ordinary quantum field theory, one can define the algebra of observables in a given region in spacetime, but in the presence of gravity, it is expected that this notion ceases to be well-defined. A substitute that appears to make sense in the presence of gravity and that also is more operationally meaningful is to consider the algebra of observables along the timelike worldline of an observer. It is known that such an algebra can be defined in quantum field theory, and the timelike tube theorem of quantum field theory suggests that such an algebra is a good substitute for what in the absence of gravity is the algebra of a region. The static patch in de Sitter space is a concrete example in which it is useful to think in these terms and to explicitly incorporate an observer in the description.
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We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer "torsion." Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.
It is shown that in elliptic cohomology — as recently formulated in the mathematical literature — the supercharge of the supersymmetric nonline
Chromodynamics with $n$ flavors of massless quarks is invariant under chiral $\mathrm{U}(n)\ensuremath{\bigotimes}\mathrm{U}(n)$. It is shown that in the limit of a large number of colors, under reasonable assumptions, this symmetry group must spontaneously break down to diagonal $\mathrm{U}(n)$.
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.
No abstract is provided for this article.
No abstract is provided for this article.
We interpret certain strong coupling singularities of the E 8 ×E 8 heterotic string on K3 in terms of exotic six-dimensional theories in which E 8 is a gauge symmetry. These theories are closely related to theories obtained at small instanton singularities, which have E 8 as a global symmetry.
