750 research outputs found
The Unbearable Beingness of Light, Dressing and Undressing Photons in Black Hole Spacetimes
Gravitational tidal forces acting on the virtual e+ e- cloud surrounding a
photon endow spacetime with a non-trivial refractive index. This has remarkable
properties unique to gravitational theories including superluminal
low-frequency propagation, in apparent violation of causality, and
amplification of the renormalized photon field, in apparent violation of
unitarity. Using the geometry of null congruences and the Penrose limit, we
illustrate these phenomena and their resolution by tracing the history of a
photon as it falls into the near-singularity region of a black hole.Comment: 8 pages, Essay awarded third prize in the Gravity Research Foundation
essay competition 201
Quantizing SL(N) Solitons and the Hecke Alegbra
The problem of quantizing a class of two-dimensional integrable quantum field
theories is considered. The classical equations of the theory are the complex
affine Toda equations which admit soliton solutions with real masses.
The classical scattering theory of the solitons is developed using Hirota's
solution techniques. A form for the soliton -matrix is proposed based on the
constraints of -matrix theory, integrability and the requirement that the
semi-classical limit is consistent with the semi-classical WKB quantization of
the classical scattering theory. The proposed -matrix is an intertwiner of
the quantum group associated to , where the deformation parameter is a
function of the coupling constant. It is further shown that the -matrix
describes a non-unitary theory, which reflects the fact that the classical
Hamiltonian is complex. The spectrum of the theory is found to consist of the
basic solitons, scalar states (or breathers) and excited (or `breathing')
solitons. It is also noted that the construction of the -matrix is valid for
any representation of the Hecke algebra, allowing the definition of restricted
-matrices, in which case the theory is unitary.Comment: 35 page
The exact mass-gaps of the principal chiral models
An exact expression for the mass-gap, the ratio of the physical particle mass
to the -parameter, is found for the principal chiral sigma models
associated to all the classical Lie algebras. The calculation is based on a
comparison of the free-energy in the presence of a source coupling to a
conserved charge of the theory computed in two ways: via the thermodynamic
Bethe Ansatz from the exact scattering matrix and directly in perturbation
theory. The calculation provides a non-trivial test of the form of the exact
scattering matrix.Comment: 11 pages, (macro included), CERN-TH.7164/94, SWAT/93-94/2
Reality of Complex Affine Toda Solitons
There are infinitely many topological solitons in any given complex affine
Toda theories and most of them have complex energy density. When we require the
energy density of the solitons to be real, we find that the reality condition
is related to a simple ``pairing condition.'' Unfortunately, rather few soliton
solutions in these theories survive the reality constraint, especially if one
also demands positivity. The resulting implications for the physical
applicability of these theories are briefly discussed.Comment: LaTeX, 15 pages, UBTH-049
On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills
We determine the exact vacuum structure of a marginal deformation of N=4 SUSY
Yang-Mills with gauge group U(N). The Coulomb branch of the theory consists of
several sub-branches which are governed by complex curves of the form
Sigma_{n_{1}} U Sigma_{n_{2}} U Sigma_{n_{3}} of genus N=n_{1}+n_{2}+n_{3}.
Each sub-branch intersects with a family of Higgs and Confining branches
permuted by SL(2,Z) transformations. We determine the curve by solving a
related matrix model in the planar limit according to the prescription of
Dijkgraaf and Vafa, and also by explicit instanton calculations using a form of
localization on the instanton moduli space. We find that Sigma_{n} coincides
with the spectral curve of the n-body Ruijsenaars-Schneider system. Our results
imply that the theory on each sub-branch is holomorphically equivalent to
certain five-dimensional gauge theory with eight supercharges. This equivalence
also implies the existence of novel confining branches in five dimensions.Comment: LaTeX file. 48 page
An integrable deformation of the AdS5Ă—S5superstring
The S-matrix on the world-sheet theory of the string in AdS5 x S5 has
previously been shown to admit a deformation where the symmetry algebra is
replaced by the associated quantum group. The case where q is real has been
identified as a particular deformation of the Green-Schwarz sigma model. An
interpretation of the case with q a root of unity has, until now, been lacking.
We show that the Green-Schwarz sigma model admits a discrete deformation which
can be viewed as a rather simple deformation of the F/F_V gauged WZW model,
where F=PSU(2,2|4). The deformation parameter q is then a k-th root of unity
where k is the level. The deformed theory has the same equations-of-motion as
the Green-Schwarz sigma model but has a different symplectic structure. We show
that the resulting theory is integrable and has just the right amount of
kappa-symmetries that appear as a remnant of the fermionic part of the original
gauge symmetry. This points to the existence of a fully consistent deformed
string background.Comment: 23 pages, improved and expanded discussion of metric and B fiel
Causality, renormalizability and ultra-high energy gravitational scattering
The amplitude A(s,t) for ultra-high energy scattering can be found in the
leading eikonal approximation by considering propagation in an Aichelburg-Sexl
gravitational shockwave background. Loop corrections in the QFT describing the
scattered particles are encoded for energies below the Planck scale in an
effective action which in general exhibits causality violation and Shapiro time
advances. In this paper, we use Penrose limit techniques to calculate the full
energy dependence of the scattering phase shift Theta_scat(hat_s},, where the
single variable hat_s = Gs/m^2 b^(d-2) contains both the CM energy s and impact
parameter b, for a range of scalar QFTs in d dimensions with different
renormalizability properties. We evaluate the high-energy limit of
Theta_scat(hat_s) and show in detail how causality is related to the existence
of a well-defined UV completion. Similarities with graviton scattering and the
corresponding resolution of causality violation in the effective action by
string theory are briefly discussed.Comment: 23 page
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