687 research outputs found
Sub-subleading soft gravitons: New symmetries of quantum gravity?
Due to seminal works of Weinberg, Cachazo and Strominger we know that tree
level quantum gravity amplitudes satisfy three factorization constraints.
Building on previous works which relate two of these constraints to symmetries
of quantum gravity at null infinity, we present rather strong evidence that the
third constraint is also equivalent to a new set of symmetries of
(perturbative) quantum gravity. Our analysis implies that the symmetry group of
quantum gravity may be even richer than the BMS group (or infinite dimensional
extension thereof) previously considered.Comment: 5 page
The Hamiltonian constraint in Polymer Parametrized Field Theory
Recently, a generally covariant reformulation of 2 dimensional flat spacetime
free scalar field theory known as Parameterised Field Theory was quantized
using Loop Quantum Gravity (LQG) type `polymer' representations. Physical
states were constructed, without intermediate regularization structures, by
averaging over the group of gauge transformations generated by the constraints,
the constraint algebra being a Lie algebra. We consider classically equivalent
combinations of these constraints corresponding to a diffeomorphism and a
Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our
treatment of the quantum constraints parallels that of LQG and obtains the
following results, expected to be of use in the construction of the quantum
dynamics of LQG:(i) the (triangulated) Hamiltonian constraint acts only on
vertices, its construction involves some of the same ambiguities as in LQG and
its action on diffeomorphism invariant states admits a continuum limit (ii)if
the regulating holonomies are in representations tailored to the edge labels of
the state, all previously obtained physical states lie in the kernel of the
Hamiltonian constraint, (iii) the commutator of two (density weight 1)
Hamiltonian constraints as well as the operator correspondent of their
classical Poisson bracket converge to zero in the continuum limit defined by
diffeomorphism invariant states, and vanish on the Lewandowski- Marolf (LM)
habitat (iv) the rescaled density 2 Hamiltonian constraints and their
commutator are ill defined on the LM habitat despite the well defined- ness of
the operator correspondent of their classical Poisson bracket there (v) there
is a new habitat which supports a non-trivial representation of the Poisson-
Lie algebra of density 2 constraintsComment: 53 page
Asymptotic Symmetries and Subleading Soft Photon Theorem in Effective Field Theories
In [1,2] it was shown that the subleading soft photon theorem in tree level
amplitudes in massless QED is equivalent to a new class of symmetries of the
theory parameterized by a vector field on the celestial sphere. In this paper,
we extend these results to the subleading soft photon theorem in any Effective
Field Theory containing photons and an arbitrary spectrum of massless
particles. We show that the charges associated to the above class of symmetries
are sensitive to certain three point functions of the theory and are corrected
by irrelevant operators of specific dimensions. Our analysis shows that the
subleading soft photon theorem in any tree level scattering amplitude is a
statement about asymptotic symmetries of the -matrix.Comment: 26 pages, 3 figure
The Diffeomorphism Constraint Operator in Loop Quantum Gravity
We construct the smeared diffeomorphism constraint operator at finite
triangulation from the basic holonomy- flux operators of Loop Quantum Gravity,
evaluate its continuum limit on the Lewandowski- Marolf habitat and show that
the action of the continuum operator provides an anomaly free representation of
the Lie algebra of diffeomorphisms of the 3- manifold. Key features of our
analysis include: (i) finite triangulation approximants to the curvature,
of the Ashtekar- Barbero connection which involve not only small
loop holonomies but also small surface fluxes as well as an explicit dependence
on the edge labels of the spin network being acted on (ii) the dependence of
the small loop underlying the holonomy on both the direction and magnitude of
the shift vector field (iii) continuum constraint operators which do {\em not}
have finite action on the kinematic Hilbert space, thus implementing a key
lesson from recent studies of parameterised field theory by the authors.
Features (i) and (ii) provide the first hints in LQG of a conceptual
similarity with the so called "mu- bar" scheme of Loop Quantum Cosmology. We
expect our work to be of use in the construction of an anomaly free quantum
dynamics for LQG.Comment: 37 pages, 6 figure
Loop Corrected Soft Photon Theorem as a Ward Identity
Recently Sahoo and Sen obtained a series of remarkable results concerning
sub-leading soft photon and graviton theorems in four dimensions. Even though
the S- matrix is infrared divergent, they have shown that the sub-leading soft
theorems are well defined and exact statements in QED and perturbative Quantum
Gravity. However unlike the well studied Cachazo-Strominger soft theorems in
tree-level amplitudes, the new sub-leading soft expansion is at the order ln
{\omega} (where {\omega} is the soft frequency) and the corresponding soft
factors structurally show completely different properties then their tree-level
counterparts. Whence it is natural to ask if these theorems are associated to
asymptotic symmetries of the S-matrix. We consider this question in the context
of sub-leading soft photon theorem in scalar QED and show that there are indeed
an infinity of conservation laws whose Ward identities are equivalent to the
loop-corrected soft photon theorem. This shows that in the case of four
dimensional QED, the leading and sub-leading soft photon theorems are
equivalent to Ward identities of (asymptotic) charges.Comment: 33 pages, no figure
New symmetries for the Gravitational S-matrix
In [15] we proposed a generalization of the BMS group G which is a semidirect
product of supertranslations and smooth diffeomorphisms of the conformal
sphere. Although an extension of BMS, G is a symmetry group of asymptotically
flat space times. By taking G as a candidate symmetry group of the quantum
gravity S-matrix, we argued that the Ward identities associated to the
generators of Diff(S^2) were equivalent to the Cachazo-Strominger subleading
soft graviton theorem. Our argument however was based on a proposed definition
of the Diff(S^2) charges which we could not derive from first principles as G
does not have a well defined action on the radiative phase space of gravity.
Here we fill this gap and provide a first principles derivation of the
Diff(S^2) charges. The result of this paper, in conjunction with the results of
[4, 15] prove that the leading and subleading soft theorems are equivalent to
the Ward identities associated to G.Comment: 19 page
Asymptotic symmetries of QED and Weinberg's soft photon theorem
Various equivalences between so-called soft theorems which constrain
scattering amplitudes and Ward identities related to asymptotic symmetries have
recently been established in gauge theories and gravity. So far these
equivalences have been restricted to the case of massless matter fields, the
reason being that the asymptotic symmetries are defined at null infinity. The
restriction is however unnatural from the perspective of soft theorems which
are insensitive to the masses of the external particles.
In this work we remove the aforementioned restriction in the context of
scalar QED. Inspired by the radiative phase space description of massless
fields at null infinity, we introduce a manifold description of time-like
infinity on which the asymptotic phase space for massive fields can be defined.
The "angle dependent" large gauge transformations are shown to have a well
defined action on this phase space, and the resulting Ward identities are found
to be equivalent to Weinberg's soft photon theorem.Comment: 19 pages, no figure
Asymptotic symmetries and subleading soft graviton theorem
Motivated by the equivalence between soft graviton theorem and Ward
identities for the supertranslation symmetries belonging to the BMS group, we
propose a new extension (different from the so-called extended BMS) of the BMS
group which is a semi-direct product of supertranslations and Diff(S^2). We
propose a definition for the canonical generators associated to the smooth
diffeomorphisms and show that the resulting Ward identities are equivalent to
the subleading soft graviton theorem of Cachazo and Strominger.Comment: 25 pages, published versio
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