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SUMMARY:Counting and constraining local four photon and four graviton S-ma
trices
DTSTART;VALUE=DATE-TIME:20191022T060000Z
DTEND;VALUE=DATE-TIME:20191022T070000Z
DTSTAMP;VALUE=DATE-TIME:20210127T104526Z
UID:indico-event-7413@cern.ch
DESCRIPTION:We study the space of all kinematically allowed four photon an
d four graviton S-matrices\, polynomial in scattering momenta. We demonstr
ate that this space is permutation invariant sector of a module over the r
ing of polynomials of the Mandelstam invariants s\, t and u. We construct
these modules for every value of the spacetime dimension D\, and so explic
itly count and parametrize the most general four photon and four graviton
S-matrix at any given derivative order. We also explicitly list the local
Lagrangians that give rise to these S-matrices. We then conjecture that th
e Regge growth of S-matrices in all physically acceptable classical theori
es is bounded by s2 at fixed t. In the case of photons a four parameter su
bset of the polynomial S-matrices constructed above satisfies this Regge c
riterion. In the case of gravity\, on the other hand\, no polynomial addit
ion to the Einstein S-matrix obeys this bound for D ≤ 6. When D ≥ 7 th
ere is a single six derivative polynomial Lagrangian consistent with our c
onjectured Regge growth bound. Our conjecture then implies that the Einste
in four graviton S-matrix does not admit any physically acceptable polynom
ial modifications for $D\\leq 6$. A preliminary analysis suggests any fini
te sum of pole exchange contributions to four graviton scattering also suc
h violates our conjectured Regge growth bound\, at least when D ≤ 6$\, e
ven when the exchanged particles have low spin.\n\nhttps://indico.tifr.res
.in/indico/conferenceDisplay.py?confId=7413
LOCATION: A 304
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7413
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