String theory and quantum gravity


String theory is the only known theory that consistently unifies all four fundamental interactions: the electromagnetic, gravitational and strong and weak nuclear forces. Its consistency with quantum mechanics makes it also the leading candidate for quantum gravity theory. String theory faces two major challenges which might be related to each other: it can allow our universe to have too many distinct physical properties (such as the masses and coupling constants of elementary particles) and therefore lack of clear experimental predictions. The second major challenge is a lack of proper non-perturbative formulation which would define the theory also in the regime of extreme quantum behavior such as at the beginning of our universe or deep within black holes.


One promising direction to address the second challenge is quantum field theoretic formulation of string theory that goes by the name of String Field Theory. There are variants of this theory for open and closed strings and also for the simpler bosonic string and more realistic supersymmetric string. In some cases (notably closed superstring) even such a description is missing. The main goals of string field theory is to understand the classical backgrounds which present us with rather novel phenomena such as emergence of extended objects called D-branes or possibly non-smooth transitions in space-time geometry and/or topology.

Another fascinating property of string theory which is believed to be present in any consistent quantum gravity theory is holography. The holographic principle states roughly that the physics of quantum gravitational system can be described by degrees of freedom living on the boundary of the system only. For some gravitational systems, this boundary theory is explicitly known and can be used to probe some of the big questions in quantum gravity, ranging from the quantum structure of black holes to the resolution of the big bang singularity by quantum effects.

One such question pertains to the microscopic origin of the entropy of black holes which was predicted by Bekenstein and Hawking. Holography has proven highly successful in enumerating these microstates, but it also predicts that individual microstates should have a realization as semiclassical geometries. The construction of such microstate solutions is an active area of current research.

Some very interesting explicit examples of holography, which have emerged in recent years, involve higher spin gravity theories which share many qualitative features with string theory. In these examples the boundary theory is relatively simple and thus they provide useful toy models for studying quantum gravity effects. In the context of 2+1 dimensional gravity with higher spins the holographic duals are two-dimensional conformal field theories with extended higher spin symmetries, which play an important role and appear in many different areas of mathematical physics, including integrable hierarchies, matrix models, instanton partition functions in supersymmetric field theories and topological strings.

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