TY - JOUR
T1 - Cauchy Conformal Fields in Dimensions d> 2
AU - Friedan, Daniel
AU - Keller, Christoph A.
N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d> 2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface. We classify all the unitary Cauchy fields. By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function. We also discuss the possibility of non-unitary Cauchy fields and classify them in d = 3 and 4.
AB - Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d> 2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface. We classify all the unitary Cauchy fields. By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function. We also discuss the possibility of non-unitary Cauchy fields and classify them in d = 3 and 4.
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U2 - 10.1007/s00220-015-2547-x
DO - 10.1007/s00220-015-2547-x
M3 - Article
AN - SCOPUS:84955313672
SN - 0010-3616
VL - 348
SP - 655
EP - 694
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -