Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe world sheet revisited
55
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the mathematical structure of the world sheet in two-dimensional conformal field theories.
rate research
Read More
The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the algebra combined with a twist that reproduces the C-bracket of double field theory. We further compare our derivation to an analysis in terms of marginal deformations as well as vertex operator algebras.
In this talk I give a preliminary account of original results, obtained in collaboration with John Ellis. Details and further elaboration will be presented in a forthcoming publication. We present a proposal for a non-critical (Liouville) string approach to confinement of four-dimensional (non-abelian) gauge theories, based on recent developments on the subject by Witten and Maldacena. We discuss the effects of vortices and monopoles on the open world-sheets whose boundaries are Wilson loops of the target-space (non Abelian) Gauge theory. By appropriately employing `D-particles, associated with the target-space embedding of such defects, we argue that the apprearance of five-dimensional Anti-De-Sitter (AdS) space times is quite natural, as a result of Liouville dressing.We isolate the world-sheet defect contributions to the Wilson loop by constructing an appropriate observable, which is the same as the second observable in the supersymmetric U(1) theory of Awada and Mansouri, but in our approach supersymmetry is not necessary.When vortex condensation occurs, we argue in favour of a (low-temperature) confining phase, in the sense of an area law, for a large-$N_c$ (conformal) gauge theory at finite temperatures. A connection of the Berezinski-Kosterlitz-Thouless (BKT) transitions on the world-sheet with the critical temperatures in the thermodynamics of Black Holes in the five-dimensional AdS space is made.
We initiate the computation of the 2-loop quantum AdS_5 x S^5 string corrections on the example of a certain string configuration in S^5 related by an analytic continuation to a folded rotating string in AdS_5 in the ``long string limit. The 2-loop term in the energy of the latter should represent the subleading strong-coupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the kappa-symmetry gauge. While we are unable to verify the cancellation of 2d UV divergences we compute the bosonic contribution to the effective action and also determine the non-trivial finite part of the fermionic contribution. Both the bosonic and the fermionic contributions to the string energy happen to be proportional to the Catalans constant. The resulting value for 2-loop superstring prediction for the subleading coefficient a_2 in the scaling function matches the numerical value found in hep-th/0611135 from the BES equation.
The principal results of the classic analysis of the shearing sheet and swing amplification by Julian & Toomre (1966) are re-derived in a more accessible way and then used to gain a better quantitative understanding of the dynamics of stellar discs. The axisymmetric limit of the shearing sheet is derived and used to re-derive Kalnajs 1965 dispersion relation and Toomres 1964 stability criterion for axisymmetric disturbances. Using the shearing sheet to revisit Toomres important 1969 paper on the group velocity implied by Lin-Shu-Kalnajs dispersion relation, we discover that two rather than one wavepackets emerges inside corotation: one each side of the inner Lindblad resonance. Although LSK dispersion relation provides useful interpretations of both wavepackets, the shearing sheet highlights the limitations of the LSK approach to disc dynamics. Disturbances by no means avoid an annulus around corotation, as the LSK dispersion relation implies. While disturbances of the shearing sheet have a limited life in real space, they live on much longer in velocity space, which Gaia allows us to probe extensively. C++ code is provided to facilitate applications of winding spiral waves.
We present a new construction for the Hodge operator for differential manifolds based on a Fourier (Berezin)-integral representation. We find a simple formula for the Hodge dual of the wedge product of differential forms, using the (Berezin)-convolution. The present analysis is easily extended to supergeometry and to non-commutative geometry.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
