Back to Search
Start Over
Scale Anomalies, States, and Rates in Conformal Field Theory
- Source :
- JHEP 04 (2017) 171
- Publication Year :
- 2016
-
Abstract
- This paper presents two methods to compute scale anomaly coefficients in conformal field theories (CFTs), such as the c anomaly in four dimensions, in terms of the CFT data. We first use Euclidean position space to show that the anomaly coefficient of a four-point function can be computed in the form of an operator product expansion (OPE), namely a weighted sum of OPE coefficients squared. We compute the weights for scale anomalies associated with scalar operators and show that they are not positive. We then derive a different sum rule of the same form in Minkowski momentum space where the weights are positive. The positivity arises because the scale anomaly is the coefficient of a logarithm in the momentum space four-point function. This logarithm also determines the dispersive part, which is a positive sum over states by the optical theorem. The momentum space sum rule may be invalidated by UV and/or IR divergences, and we discuss the conditions under which these singularities are absent. We present a detailed discussion of the formalism required to compute the weights directly in Minkowski momentum space. A number of explicit checks are performed, including a complete example in an 8-dimensional free field theory.<br />Comment: 39 pages, 7 figures
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- JHEP 04 (2017) 171
- Publication Type :
- Report
- Accession number :
- edsarx.1612.07800
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP04(2017)171