18,628 research outputs found
Nonrelativistic Conformal Field Theories in the Large Charge Sector
We study Schr\"odinger invariant field theories (nonrelativistic conformal
field theories) in the large charge (particle number) sector. We do so by
constructing the effective field theory (EFT) for a Goldstone boson of the
associated symmetry in a harmonic potential. This EFT can be studied
semi-classically in a large charge expansion. We calculate the dimensions of
the lowest lying operators, as well as correlation functions of charged
operators. We find universal behavior of three point function in large charge
sector. We comment on potential applications to fermions at unitarity and
critical anyon systems.Comment: 24 page
The Brauer-Manin obstruction to the local-global principle for the embedding problem
We study an analogue of the Brauer-Manin obstruction to the local-global
principle for embedding problems over global fields. We will prove the
analogues of several fundamental structural results. In particular we show that
the (algebraic) Brauer-Manin obstruction is the only one to weak approximation
when the embedding problem has abelian kernel. As a part of our investigations
we also give a new, elegant description of the Tate duality pairing and prove a
new theorem on the cup product.Comment: Referenced upgraded. 37 page
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