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Person# Gabriel Francisco Cuomo

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A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformati

In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. Th

In theoretical physics, the scaling dimension, or simply dimension, of a local operator in a quantum field theory characterizes the rescaling properties of the operator under spacetime dilations

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Gil Badel, Gabriel Francisco Cuomo, Alexander Monin, Riccardo Rattazzi

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U (1) model at the Wilson-Fisher fixed point in D = 4 - epsilon can be computed semiclassically for arbitrary values of lambda n, where lambda is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the U (1) model in 3 - epsilon dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal O(n(0)) contribution to the scaling dimension of large charge operators in 3D CFTs. (C) 2020 Published by Elsevier B.V.

2020In this letter, we discuss certain universal predictions of the large charge expansion in conformal field theories with U (1) symmetry, mainly focusing on four-dimensional theories. We show that, while in three dimensions quantum fluctuations are responsible for the existence of a theory-independent Q(0) term in the scaling dimension Delta(Q) of the lightest operator with fixed charge Q >> 1, in four dimensions the same mechanism provides a universal Q(0) log Q correction to Delta(Q). Previous works discussing fourdimensional theories failed in identifying this term. We also compute the first subleading correction to the OPE coefficient corresponding to the insertion of an arbitrary primary operator with small charge q < Q in between the minimal energy states with charge Q and Q + q, both in three and four dimensions. This contribution does not depend on the operator insertion and, similarly to the quantum effects in Delta(Q), in four dimensions it scales logarithmically with Q. (C) 2020 The Author. Published by Elsevier B.V.

Gabriel Francisco Cuomo, Angelo Esposito, Alexander Monin, Riccardo Rattazzi

At finite density, the spontaneous breakdown of an internal non-Abelian symmetry dictates, along with gapless modes, modes whose gap is fixed by the algebra and proportional to the chemical potential: the gapped Goldstones. Generically the gap of these states is comparable to that of other non-universal excitations or to the energy scale where the dynamics is strongly coupled. This makes it non-straightforward to derive a universal effective field theory (EFT) description realizing all the symmetries. Focusing on the illustrative example of a fully broken SU(2) group, we demonstrate that such an EFT can be constructed by carving out around the Goldstones, gapless and gapped, at small 3-momentum. The rules governing the EFT, where the gapless Goldstones are soft while the gapped ones are slow, are those of standard nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the EFT Lagrangian formally preserves gapped Goldstone number, and processes where such number is not conserved are described inclusively by allowing for imaginary parts in the Wilson coefficients. Thus, while the symmetry is manifestly realized in the EFT, unitarity is not. We comment on the application of our construction to the study of the large charge sector of conformal field theories with non-Abelian symmetries.