Perturbative and non-perturbative aspects of pure Script N = 1 super Yang-Mills theory from wrapped branes

Abstract

The Maldacena-Nuñez solution is generalized to include a number of integration constants, one of which controls the resolution of the singularity of the wrapped D5-brane background. Some features of the dual pure N = 1 super Yang-Mills (SYM) theory are calculated, amongst which the gluino condensate, the beta function of the gauge coupling and a brane probe potential, which is related to the Veneziano-Yankielowicz effective potential. Each integration constant has a precise meaning in the dual SYM theory, e.g., the amount of non-perturbative SYM physics captured by the gravity configuration is described by the singularity resolution parameter.

Bulk dynamics in confining gauge theories

“…We have, at present, no specific interpretation of their role, although the 17 In the 10-d MN solution, the location of the Dirac string for the magnetic 2-form C 2 is specified by an angular variable ψ that can take 2N different values for the same field theory θ-angle, but the solution is symmetric under a shift by π of ψ, leaving N different configurations. Equivalently, one has N different ways of placing probe D5-branes in the background, in order to obtain the same field theory action [25,27,29].…”

“…Another example is the wrapped D5-brane, also known as the Maldacena-Nunez (MN) solution [25]. In the infrared, it shares many properties with N = 1 SYM theory [26,27,28,29], but it becomes six-dimensional little string theory in the UV. We are mostly interested in the KS solution, since there the supergravity approximation is under full control.…”

Gauge Theories from D Branes

“…φ = −φ (8.96) keeping ρ and ψ fixed. If we now compute the gauge couplings on the cycle specified in the previous equation we get [37,38,39] These two Eq.s must be considered together with the relation between ρ and the renormalization group scale given in Eq. (8.80), which in the following we are going to derive.…”

“…A natural and elegant way to solve the previous problems is presented in Ref.s [37,38,39] and is based on the observation that the correct cycle, i.e. the one that is topologically nontrivial is not the cycle chosen in Ref.…”