On the infrared divergence and global colour in N $$ \mathcal{N} $$ = 4 Yang-Mills theory
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Springer
Received: April 1, 2020 Accepted: June 29, 2020 Published: July 30, 2020
Su Yu Ding, Joanna Karczmarek and Gordon W. Semenoff Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada
E-mail: [email protected], [email protected], [email protected] Abstract: The N = 4 superconformal Yang-Mills theory on flat four-dimensional Minkowski space is a de-confined gauge theory in the sense that the string tension for fundamental representation coloured quarks vanishes. In fact, static fundamental representation quarks which lie in certain half-BPS super-multiplets do not interact at all. An interesting question asks whether such quarks would carry a well-defined global colour charge which, when the gauge is fixed, should have the status of an internal symmetry. We shall present a simple paradigmatic model which suggests that the answer to this question lies in the way in which infrared divergences are dealt with. Keywords: Scattering Amplitudes, Wilson, ’t Hooft and Polyakov loops ArXiv ePrint: 2003.11114
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)228
JHEP07(2020)228
On the infrared divergence and global colour in N = 4 Yang-Mills theory
Contents 1
2 Heavy quark with constant acceleration 2.1 Wilson line for an accelerating trajectory
4 7
3 Soft particle emission 3.1 Bremsstrahlung and recovering unitarity 3.2 Introducing a detector resolution 3.3 Introducing a fundamental infrared cutoff
9 9 12 14
4 Dressed states
14
5 Conclusions
17
A The matrix model sums ladder diagrams A.1 One-point function A.2 Two-point function
18 18 19
B Infrared cutoff integration
20
C Integral I
21
D Integral II = Integral III
22
E Integral IV
22
1
Introduction
There is a fundamental issue as to whether the S matrix exists and whether it can be a useful tool for the study of four dimensional quantum field theories where the interactions are mediated by massless fields. Such interactions do not decouple sufficiently rapidly at large distances and times to justify the assumption that particles become free so that the S-matrix can be used to describe transitions between free particle states. If one ignores the problem and proceeds to compute amplitudes using the standard diagrammatic perturbation theory, the difficulty is manifest as infrared and co-linear divergences. In Abelian gauge theories such as quantum electrodynamics, techniques for dealing with infrared divergences are well known. There are two principal approaches, either the computation of transition probabilities inclusive of soft photon production [1]–[3] or the use of the S matrix to compute transition amplitudes between dressed states [4]–[10]. They
–1–
JHEP07(2020)228
1 Introduction
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JHEP07(2020)228
give identical results for transition probabilities. However, it has recently been pointed out [11]–[17] that the two approaches have subtle differences with how quantum information is distributed in a scattering process
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