Dynamical symmetry breaking in SYM theories as a non-semiclassical effect

Abstract

We study supersymmetry breaking effects in N = 1 SYM from the point of view of quantum effective actions. Restrictions on the geometry of the effective potential from superspace are known to be problematic in quantum effective actions, where explicit supersymmetry breaking can and must be studied. On the other hand the true ground state can be determined from this effective action, only. We study whether some parts of superspace geometry are still relevant for the effective potential and discuss whether the ground states found this way justify a low energy approximation based on this geometry. The answer to both questions is negative: Essentially nonsemiclassical effects change the behavior of the auxiliary fields completely and demand for a new interpretation of superspace geometry. These non-semiclassical effects can break supersymmetry.

Applying the Cho–Duam–Ge decomposition to supersymmetric QCD

“…All possible gauge transformations can be expressed as a linear combination of these two [23]. Two equations, either (10) or (11), are sufficient to determine the gauge transformation of all the CDG components of the gluon field because they can all be expressed in terms of A μ and the ni by…”

“…Another study [8] found that SUSY was broken in SQCD when the number of flavours was less than the number of colours. A later study of the thermodynamic limits of SQCD [9] found that confinement implies SUSY breaking, and another [10] makes a careful study of the superspace geometry to conclude that SUSY is dynamically broken by non-semiclassical effects that transform auxiliary fields into dynamic ones. (This summary is by no means definitive and readers are also directed to the references within these citations, and to reviews such as [11][12][13][14][15].…”