TY - JOUR

T1 - Infrared behavior at negative curvature

AU - Callan, Curtis G.

AU - Wilczek, Frank

N1 - Funding Information:
* Research supported in part by DOEcontract DE-AC02-84-15534. * * Research supported in part by DOE grant DE-FG02-90ER40542.

PY - 1990

Y1 - 1990

N2 - It is argued that constant negative curvature provides a very convenient infrared regulator for interacting euclidean quantum field theories. The two-dimensional XY model on a space with such curvature is disordered at arbitrarily small non-zero temperatures by topologically non-trivial fluctuations (vortices), even though the effect of perturbative fluctuations (spin-waves) is negligible at large distances. Similarly, constant negative curvature brings the infrared behavior of QCD (as well as the ultraviolet behavior, of course) under analytic control without any conflict with gauge invariance. In particular, for weak coupling there is a unique single instanton solution and the instanton gas is truly dilute.

AB - It is argued that constant negative curvature provides a very convenient infrared regulator for interacting euclidean quantum field theories. The two-dimensional XY model on a space with such curvature is disordered at arbitrarily small non-zero temperatures by topologically non-trivial fluctuations (vortices), even though the effect of perturbative fluctuations (spin-waves) is negligible at large distances. Similarly, constant negative curvature brings the infrared behavior of QCD (as well as the ultraviolet behavior, of course) under analytic control without any conflict with gauge invariance. In particular, for weak coupling there is a unique single instanton solution and the instanton gas is truly dilute.

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U2 - 10.1016/0550-3213(90)90451-I

DO - 10.1016/0550-3213(90)90451-I

M3 - Article

AN - SCOPUS:0000593726

SN - 0550-3213

VL - 340

SP - 366

EP - 386

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2-3

ER -