The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi^2 with bulk interaction Phi^4.
For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the inequality holds for time asymmetric data in spherical symmetry. Our analysis is motivated by the constant-negative-spatial-curvature form of the AdS black hole metric.
We study a solution of the Einstein's equations generated by a self-gravitating, anisotropic, static, non-singular matter fluid. The resulting Schwarzschild like solution is regular and accounts for smearing effects of noncommutative fluctuations of the geometry. We call this solution regular Schwarzschild spacetime. In the presence of an Anti-deSitter cosmological term, the regularized metric offers an extension of the Hawking-Page transition into a van der Waals-like phase diagram. Specifically the regular Schwarzschild-Anti-deSitter geometry undergoes a first order small/large black hole tr…
Brane Constructions, Fractional Branes and Anti-deSitter Domain Walls
AdS 5 x X 5上的IIB型弦论的紧化，其中X 5是爱因斯坦空间，对于X 5的某些选择，可以有1/4或1/2的最大超对称性。这些理论中的一些承认奇异的畴壁产生于X5中包裹2-圈的5-膜。我们探讨这些畴壁，分数膜和膜拉伸的间隔之间的关系。包裹膜中的世界体积通量在分析中起着重要的作用。我们画了一些相似之处的AdS背景与异国情调的域壁和N=1超对称MQCD，并确定其他扩展对象的AdS侧的双膜建设。膜创建的过程是用来给分数膜和膜之间的关系的间隔的替代推导。
In this paper we study the propagator of a vector fields on a euclidean maximally-symmetric background in arbitrary space-time dimensions. We study two cases of interest: Massive and massless vector fields. In each case we computed the propagator of the vector fields on euclidean deSitter background, isolating the transverse and longitudinal part. In both case of massive and massless vector fields, the short distance limit of the full propagator agrees with the flat space-time propagator. In the case of massive propagator, the transverse part has a well defined massless limit, and in this limi…
We argue that flat space amplitudes for the process $ 2 \to n$ gravitons at center of mass energies $\sqrt{s}$ much less than the Planck scale, will coincide approximately with amplitudes calculated from correlators of a boundary CFT for AdS space of radius $R\gg L_P$, only when $n < R/L_P$ . For larger values of $n$ in AdS space, insisting that all the incoming energy enters "the arena" [arXiv:hep-th/9901079], implies the production of black holes, whereas there is no black hole production in the flat space amplitudes. We also argue, from unitarity, that flat space amplitudes for all $n$ are …
We study the constraints on HST models of AdS space-time. The causal diamonds of HST along time-like geodesics of AdS space-time, fit nicely into the FRW patch of AdS space. The coordinate singularity of the FRW patch is identified with the proper time at which the Hilbert space of the causal diamond becomes infinite dimensional. For diamonds much smaller than the AdS radius, RAdS, the time dependent Hamiltonians of HST are the same as those used to describe similar diamonds in Minkowski space. In particular, they are invariant under the fuzzy analog of volume preserving diffeomorphisms of the…
We reconsider the one loop divergence of ${\cal N}=8$ supergravity in four dimensions. We compute the finite effective potential of ${\cal N}=8$ anti-deSitter supergravity and interpret it as logarithmic running of the cosmological constant. We find that quantum inequivalence between fields that are classically dual is due to boundary modes in AdS$_4$. Some subtleties are traced to the difference between the Euler characteristic of global and thermal AdS$_4$.
We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and background independence. We derive the equations of motion for Lie algebra valued scalars and show that in the geometric optics limit they traverse geodesics with respect to the Lorentzian geometry determined by the frame fields. Mixing between components appears to next to leading order in the WKB approximation. We then restrict to two space-time dimensions …
Action principles, restoration of BRS symmetry and the renormalization group equation for chiral non-Abelian gauge theories in dimensional renormalization with a non-anticommuting $γ_5$
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for $γ_5$. One goal is to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal is to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consisten…
We apply the BMHV scheme for non-anticommuting $γ_5$ to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. Th…
