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SUMMARY:Gravity as a Gauge Theory
DTSTART;VALUE=DATE-TIME:20130124T154500Z
DTEND;VALUE=DATE-TIME:20130124T164500Z
DTSTAMP;VALUE=DATE-TIME:20200713T121235Z
UID:indico-event-534@indico.math.cnrs.fr
DESCRIPTION:I will explain how General Relativity in four space-time dimen
sions (with cosmological constant) can be reformulated as an SU(2) gauge t
heory of a certain type. The action is a (diffeomorphism invariant) functi
onal of an SU(2) connection\; no metric is present in the formulation of t
he theory. This formulation of GR is in many ways analogous to the one pro
posed many years ago by Eddington (Eddington's Lagrangian is a function of
just the affine connection and is given by the square root of the determi
nant of the Ricci tensor). The new formulation has some remarkable propert
ies. First\, on a 4-manifold\, the space of SU(2) connections modulo gauge
transformations has just 9 components per space-time point\, as compared
to 10 components of a metric tensor. Correspondingly\, the action of the n
ew formulation can be interpreted as a functional on the space of conforma
l classes of metrics. Thus\, the conformal factor is not free to propagate
in this formulation even off-shell. This has the effect that the action f
unctional is (at least locally) convex - there is no conformal mode proble
m of the usual metric formulation of GR. Another remarkable property of th
e new formulation is that diffeomorphisms are very easy to deal with. The
most natural gauge-fixing of these does not make the corresponding compone
nts of the connection propagate. As a result\, in (linearized) quantum the
ory only 8 components of the connection propagate as compared to 10 metric
components in the usual formulation. All these 8 components fit into a si
ngle irreducible representation of the Lorentz group\, which makes the pro
pagator very simple. There are also some remarkable simplifications in the
structure of the interaction vertices. The full off-shell 3-vertex (in de
Sitter space) contains just 3 terms as compared to a couple of dozen term
s in the metric formulation. The 4-vertex is a couple of lines as compared
to a couple of pages in the standard description. As an illustration of t
he formalism I will describe how the graviton scattering amplitudes are co
mputed in this approach. \n\nThe new gauge-theoretic reformulation of GR
also leads to (an infinite-parameter) family of modified gravitational th
eories\, all propagating just two polarizations of the graviton\, as GR. T
his leads to a rather strong claim that\, in spite of the standard GR uniq
ueness theorems\, General Relativity is not the only interacting theory of
massless spin two particles. However\, GR appears to be the only parity-i
nvariant gravitational theory\, as all the "deformations of GR" can be sho
wn to be parity violating. I will also describe how matter is coupled in t
his approach\, and give some speculations as to a possible UV completion o
f gravity.\n\nhttps://indico.math.cnrs.fr/event/534/
LOCATION:Institut des Hautes Etudes Scientifiques Amphithéâtre Léon Mot
chane
URL:https://indico.math.cnrs.fr/event/534/
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