802 publications from this institution
It is argued that the ground state of the Kaluza-Klein unified theory is unstable against a process of semiclassical barrier penetration. This is related to the fact that the positive energy conjecture does not hold for the Kaluza-Klein theory; an explicit counter-example is given. The reasoning presented here assumes that in general relativity one should include manifolds of non-vacuum topology. It is argued that the existence of elementary fermions (not present in the original Kaluza-Klein theory) would stabilize the Kaluza-Klein vacuum.
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field theory -- it is a property of the algebra of observables and not just of the states.
In this talk, I survey the merits and demerits of Supersymmetry, as well as other approaches to the gauge hierarchy problem.
The first obstruction to splitting a supermanifold S is one of the three components of its super Atiyah class, the two other components being the ordinary Atiyah classes on the reduced space M of the even and odd tangent bundles of S. We evaluate these classes explicitly for the moduli space of super Riemann surfaces (super moduli space) and its reduced space, the moduli space of spin curves. These classes are interpreted in terms of certain extensions arising from line bundles on the square of the varying (super) Riemann surface. These results are used to give a new proof of the non-projectedness of ${\mathfrak{M}}_{g,1}$, the moduli space of super Riemann surfaces with one puncture.
Phase transitions are studied in M-theory and F-theory. In M-theory compactification to five dimensions on a Calabi-Yau, one can find topology-changing transitions similar to those seen in conformal field theory, but the non-geometrical phases known in conformal field theory are absent. At boundaries of moduli space where such phases might have been expected, the moduli space ends, by a conventional or unconventional physical mechanism. The unconventional mechanisms, which roughly involve the appearance of tensionless strings, can sometimes be better understood in F-theory.
We show that QCD with a sufficient number of fermions of zero bare mass has physical massless particles. That result also follows from triangle anomalies,
We describe a mechanism for using discrete symmetries to solve the doublet-triplet splitting problem of four-dimensional supersymmetric GUT's. We present two versions of the mechanism, one via ``deconstruction,'' and one in terms of M-theory compactification to four dimensions on a manifold of G_2 holonomy.
No abstract is provided for this article.
This paper summarizes our rather lengthy paper, Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions, and is meant to be an informal, yet detailed, introduction and summary of that larger work.
No abstract is provided for this article.
The Langlands program of number theory, or what we might call Langlands duality, was proposed in more or less its present form by Robert Langlands, in the late 1960s. It is a kind of unified scheme for many results in number theory ranging from quadratic reciprocity, which is hundreds of years old, to modern results such as Andrew Wiles’ proof of Fermat’s last theorem, which involved a sort of special case of the Langlands program. For today, however, I will not assume any prior knowledge of the Langlands program.
No abstract is provided for this article.
I sketch what it is supposed to mean to quantize gauge theory, and how this can be made more concrete in perturbation theory and also by starting with a finite-dimensional lattice approximation. Based on real experiments and computer simulations, quantum gauge theory in four dimensions is believed to have a mass gap. This is one of the most fundamental facts that makes the Universe the way it is. This article is the written form of a lecture presented at the conference Geometric Analysis: Past and Future (Harvard University, August 27-September 1, 2008), in honor of the 60th birthday of S.-T. Yau.
For vacua of string theory which leave unbroken N = 1 supersymmetry in the leading approximation, non-renormalization theorems guarantee that higher order (string or sigma model) perturbative corrections do not modify the space-time superpotential. If the low energy gauge group contains U(1) factors, this is not enough to ensure that the low energy physics is perturbatively stable. It is still possible to generate a Fayet-Iliopoulos D-term. We show that under certain conditions such a term is generated, and destabilizes the vacuum. This is a counterexample to various claims about the universal absence of quantum tadpoles when expanding around a classical solution with unbroken supersymmetry. Whether, in a given model, the generation of a D-term will destabilize the vacuum (or merely change the pattern of symmetry breaking) can be determined from properties of the low energy effective action.
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.
The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an $A$-brane of a certain simple kind can be an eigenbrane for the action of 't Hooft operators. To set the stage, we review some facts about Higgs bundles and the Hitchin fibration. We consider only the simplest examples, in which many technical questions can be avoided.
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 $N$ of positive scalar curvature. We show that under these conditions, $H_n(M;Z)=0$ and in particular $N$ must be connected. These results resolve some puzzles concerning the AdS/CFT correspondence.
We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional \mathcal{N} =4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mstyle mathvariant="script"><mml:mi>𝒩</mml:mi></mml:mstyle><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> super Yang-Mills theory on \mathbb{CP}^{2} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mstyle mathvariant="double-struck"><mml:mi>ℂ</mml:mi><mml:mi>ℙ</mml:mi></mml:mstyle><mml:mn>2</mml:mn></mml:msup></mml:math> for the gauge group SO(3) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math> from the path integral of the effective theory on the Coulomb branch. The holomorphic kernel of this equation, which receives contributions only from the instantons, is not modular but ‘mock modular’. The partition function has correct modular properties expected from S <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math> -duality only after including the anomalous nonholomorphic boundary contributions from anti-instantons. Using M-theory duality, we relate this phenomenon to the holomorphic anomaly of the elliptic genus of a two-dimensional noncompact sigma model and compute it independently in two dimensions. The anomaly both in four and in two dimensions can be traced to a topological term in the effective action of six-dimensional (2,0) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math> theory on the tensor branch. We consider generalizations to other manifolds and other gauge groups to show that mock modularity is generic and essential for exhibiting duality when the relevant field space is noncompact.
Three subjects are considered here: a self-dual non-critical string that appears in Type IIB superstring theory at points in ${\rm K3}$ moduli space where the Type IIA theory has extended gauge symmetry; a conformal field theory singularity at such points which may signal quantum effects that persist even at weak coupling; and the rich dynamics of the real world under compactification, which may be relevant to some attempts to explain the vanishing of the cosmological constant.
