TY - JOUR

T1 - Topological strings

AU - Montano, David

AU - Sonnenschein, Jacob

N1 - Funding Information:
In the beginning of this year, Witten wrote a series of papers describing the construction of topological quantum field theories (TQFT) \[1, 2\]. These are quantum field theories whose classical observables are topological invariants. Thus, in some sense, these TQFT's represent a phase of quantum field theories where general covariance is unbroken \[2\]. Witten then refers to the massless graviton as the Goldstone boson of general covariance. We have that the graviton is the fluctuation about a particular background metric (usually, Minkowski space). In the standard electroweak model considerations of renormalizability also require that the theory first be constructed in a gauge invariant symmetric phase. Perhaps then it is fruitful to formulate a theory in a phase of unbroken general covariance and then find a mechanism for the spontaneous breaking of this symmetry with the consequent generation of a graviton and thus local gravity. This may provide a nice way to maintain renormalizability and unitarity in a quantum theory of gravity and was a major motivation for our work. Here we investigate a two-dimensional non-linear sigma model in a phase of unbroken general covariance. There has been recent speculation that such a nonlinear sigma model may describe string theory above the Hagedorn temperature \[3\]. This would be a topological string theory, i.e. a string theory where only world-sheet * Work supported by the Department of Energy, contract DE-AC03-76SF00515. ** Work supported by Dr. Chaim Weizmann Postdoctoral Fellowship.

PY - 1989/2/6

Y1 - 1989/2/6

N2 - Following some recent works of Witten, we explore topological non-linear sigma models (TSM). We construct 2-D topological gravity which is then coupled to the TSM resulting in a topological bosonic string theory. This theory has a non-tachyonic vacuum and can be formulated on any even dimensional target manifold which admits some non-trivial topology. It is then shown that the metric independence of the target manifold can not be maintained at the quantum level. Quantum consistency at the one-loop level of the sigma model requires that the Ricci scalar vanishes.

AB - Following some recent works of Witten, we explore topological non-linear sigma models (TSM). We construct 2-D topological gravity which is then coupled to the TSM resulting in a topological bosonic string theory. This theory has a non-tachyonic vacuum and can be formulated on any even dimensional target manifold which admits some non-trivial topology. It is then shown that the metric independence of the target manifold can not be maintained at the quantum level. Quantum consistency at the one-loop level of the sigma model requires that the Ricci scalar vanishes.

UR - http://www.scopus.com/inward/record.url?scp=0011672987&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(89)90318-0

DO - 10.1016/0550-3213(89)90318-0

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0011672987

SN - 0550-3213

VL - 313

SP - 258

EP - 268

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2

ER -