1. 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

2. in coll. with Bruno Lima De Souza, Antonio Duarte Pereira and Stefano Giaccari

3. This talk is about: Conformal invariance CFT correlators Their regularization Contact terms and anomalies Momentum space formalism

4. 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,…)

11. a general approach: differential regularization

14. small detour: some definitions

20. back to differential regularization

21. Ambiguities are also called «contact terms»

25. The story initiates way back…. another detour is necessary

28. Trace anomaly in chiral theories (an overdue result …, JHEP 07(2014)117 )

31. Feynman rules Relevant diagrams

36. back to correlators

38. Let’s summarize the situation…

41. Let’s go to momentum space

46. 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

47. THANKS TTHT THANKS