UV/IR connection, a matrix perspective

Abstract

We show that the matrix formulation of non-commutative field theories is equivalent, in the continuum, to a formulation in a mixed configuration-momentum space. In this formulation, the non-locality of the interactions, that leads to the IR/UV mixing, becomes transparent. We clarify the relation between long range effects (and IR divergences) and the non-planarity of the corresponding Feynman diagrams.

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

“…The effective geometry of such branes (given by some matrix background 1 ) can be elaborated as noncommutative or semi-classical geometry, and fluctuations of these backgrounds lead to noncommutative gauge theory coupled to this geometry [5,6]. Here the maximal supersymmetry of the matrix model plays an important role, since otherwise unacceptable large non-local effects due to UV/IR mixing [4,7,8]) invalidate the semi-classical picture.…”

Covariant 4-dimensional fuzzy spheres, matrix models and higher spin

“…We are interested in fuzzy 4-spheres which are covariant under SO (5). They will be defined in terms of five hermitian matrices X a , a = 1, .…”

“…. , 5 acting on some finite-dimensional Hilbert space H, and transforming as vectors under SO (5) [M ab , X c ] = i(δ ac X b − δ bc X a ), [M ab , M cd ] = i(δ ac M bd − δ ad M bc − δ bc M ad + δ bd M ac ) .…”

Matrix varphi4models on the fuzzy sphere and their continuum limits

“…The problem was discussed in the Moyal plane in [7] where the fields possess an infinite number of modes, and consequently a regularization procedure is needed. This phenomenon appears to be generic for field theories in non-commutative spaces.…”