Regularization of conformal correlators

Loriano Bonora, SISSA, Trieste

LT-11, Varna

June 15-21, 2015

Loriano Bonora, SISSA, Trieste

LT-11, Varna

June 15-21, 2015

in coll. with Bruno Lima De Souza,

Antonio Duarte Pereira and Stefano Giaccari

This talk is about:

• Conformal invariance

• CFT correlators

• Their regularization

• Contact terms and anomalies

• Momentum space formalism

I will talk in particular about e.m. tensor correlators. Why are they so important?

Because the source of the e.m. tensor is the metric (or, better, the metric fluctuations). Thus the e.m. tensor correlators can be interpreted as scattering amplitudes for gravitons.

(C.Closset,D.Dumitrescu,G.Festuccia, Z.Komargodski,N.Seiberg,X.Camanho,J.Edelstein,J.Maldacena, G.Pimentel, A.Zhiboedov,…)

a general approach:differential regularization

small detour: some definitions

back to differential regularization

Ambiguities are also called «contact terms»

The story initiates way back….

another detour is necessary

Trace anomaly in chiral theories

(an overdue result…, JHEP 07(2014)117 )

Feynman rules

Relevant diagrams

back to correlators

Let’s summarize the situation…

Let’s go to momentum space

In momentum space the CA and conformal cohomology take a familiar form.

In particular contact terms can be studied in a rather simple way, because they are polynomials in the momenta.

Many Ward identities in momentum space have been solved exactly.

Now one can start a systematic (algorithmic) way to find all possible consistent contact terms.

Conclusions and prospects

THANKSTTHTTHANKS