Positivity bounds are a set of consistency conditions that EFTs shall obey in order to admit a sensible UV completion. Generically, they arise as inequalities for the Wilson coefficients of the low-energy theory and, in the Lorentz invariant framework, they are extracted exploiting the analyticity properties of the S-Matrix.

I will show how the analytic structure of the S-Matrix gets deeply modified by the presence of a spontaneous breaking of Lorentz invariance. I will discuss the results of (

Unlike the Lorentz invariant case, the resulting S-matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.

I will comment on the implications for the formulation of positivity bounds in a cosmological/condensed matter setting, including some possible future directions.

I will show how the analytic structure of the S-Matrix gets deeply modified by the presence of a spontaneous breaking of Lorentz invariance. I will discuss the results of (

*JHEP 06 (2024) 201)*, where we studied the S-matrix of Goldstones in the renormalizable theory of a U(1) complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this S-matrix exists at all energies.Unlike the Lorentz invariant case, the resulting S-matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.

I will comment on the implications for the formulation of positivity bounds in a cosmological/condensed matter setting, including some possible future directions.

## Dates:

Mardi, 29 octobre, 2024 - 14:00 to 15:00

## Localisation / Location:

APC

## Salle / Local:

483A-Malevitch

- Séminaire

## Nom/Prénom // Last name/First name:

LONGO Alessandro

## Affiliation:

SISSA, Trieste

## Equipe(s) organisatrice(s) / Organizing team(s):

- Théorie

## Pays / Country:

Italy