Abstract
We investigate whether the symmetry transformations of a bosonic string are connected by T-duality. We start with a standard closed string theory. We continue with a modified open string theory, modified to preserve the symmetry transformations possessed by the closed string theory. Because the string theory is conformally invariant world-sheet field theory, in order to find the transformations which preserve the physics, one has to demand the isomorphism between the conformal field theories corresponding to the initial and the transformed field configurations. We find the symmetry transformations corresponding to the similarity transformation of the energy-momentum tensor, and find that their generators are T-dual. Particularly, we find that the general coordinate and local gauge transformations are T-dual, so we conclude that T-duality in addition to the well-known exchanges, transforms symmetries of the initial and its T-dual theory into each other.
Highlights
One of the most important notions in theoretical physics is a symmetry
The quantization of the bosonic string theory, describing the string moving in a background consisting of a space-time metric Gμν, a Kalb–Ramond field Bμν and a dilaton field Φ, leads to the conclusion that in order to have a conformal invariance on the quantum level the energy-momentum tensor components T±(φ), with φ = (Gμν, Bμν, Φ), have to obey the Virasoro algebras [2,10,11], T±(φ(σ )), T±(φ(σ ))
We considered the general coordinate and the local gauge transformations of the bosonic string, and we showed that they are T-dual to each other
Summary
One of the most important notions in theoretical physics is a symmetry. What is a symmetry of the string theory is not yet clear mainly because the theory itself is not yet formulated in a background independent way, which would enlighten its deeper principles. The transformation will in general make changes to the world-sheet energy-momentum tensor If these changes can be interpreted as changes in the spacetime fields, the latter are the symmetry transformations of the target space. We will demand that the new energy-momentum tensor satisfies the Virasoro algebra as well This means that the transformed theory is physically equivalent to the initial theory, or that these field transformations are the symmetry of space-time theory. In this way we will find a transformation of space-time fields corresponding to a similarity transformation and the generator of this symmetry. We will consider both closed and open string theory. The symmetries are T-dual and the complete generator of symmetries is self-dual
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