Abstract
A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.
Highlights
From the physical point of view, different sectors correspond to different physical phases
Where is the contour defined to enclose all the possible complex poles of the integrand (10) lying in the upper half of the complex plane, while avoiding every possible real pole, branch point and branch cut. This new topological object is a relative of the topological object NW defined in [37], with the difference that their object is defined in terms of the propagator itself, while our N depends on the mass function M(z), which in general can be defined by writing in full generality a fermion propagator as in (3), or for a bosonic propagator
In order to explicitly show that our generalized topological object (10) can be applied to the topological analysis of bosonic relativistic quantum fields within the momentum space topology (MST) framework, we perform here the topological classification of the space defined by the two-point Green function of gluons, whose analytic expression is one that has been used in the literature to fit lattice data at zero and finite temperature, according to [13,19,39,40]
Summary
From the physical point of view, different sectors correspond to different physical phases. Momentum space topology (MST) has been applied to the classification of the ground state of relativistic quantum field theories (see [3], where MST is first applied to lattice fermions) into universality classes, without the same resonance as in condensed matter [4,5,6,7,8,9]. Up to now, topological invariants constructed in MST have not been applied to bosonic systems. Inspired by the power of MST in the classification of the vacuum of quantum field theories, we propose a new topologically invariant object that is sensitive to the. 3 we extract, departing from the standard definition, a specific representation for the MST invariant that is very useful for a generalization to the bosonic sector.
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