Abstract
We construct an efficient MonteCarlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series.
Highlights
Conformal field theories (CFTs) occupy a central place in our understanding of modern physics
We verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global Uð1Þ charge can be obtained via a series expansion in the inverse charge 1=Q
We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series
Summary
We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the Oð2Þ universality class. They describe critical phenomena in condensed matter physics and statistical models [1,2], quantum gravity via the AdS/ CFT correspondence [3], and can be found at fixed points of renormalization group flows [4,5,6,7] They are uniquely described by a set of dimensionless numbers (the CFT data), i.e., conformal dimensions and operator product expansion (OPE) coefficients associated with the primary fields of the theory. Consequence of the fact that R3 is conformally equivalent to R × S2ðr0Þ Such a connection has been used in CFTs with global Uð1Þ charges to show that the conformal dimension DðQÞ of the lowest operator with fixed Uð1Þ charge Q can be expanded in inverse powers of the charge density on a unit sphere Q=4π [15,16] (see [17,18,19,20,21] for related work), DðQÞ.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
