Spectral Action for Torsion with and without Boundaries

TY - JOUR

T1 - Spectral Action for Torsion with and without Boundaries

AU - Iochum, B.

AU - Levy, Cyril Olivier

AU - Vassilevich, D.

PY - 2012/3

Y1 - 2012/3

N2 - We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter θ of the boundary conditions, and show that θ = 0 is a critical point of the action in any dimension and at all orders of the expansion.

AB - We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter θ of the boundary conditions, and show that θ = 0 is a critical point of the action in any dimension and at all orders of the expansion.

M3 - Journal article

SN - 0010-3616

VL - 310

SP - 367

EP - 382

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -