Superstring theoryをめぐって(放談室)

Quantum field theory on noncommutative spaces

Physical Foundations of Cosmology: Preface

U duality and M theory

https://dspace.library.uu.nl/bitstream/handle/1874/7992/Loll_98_non_perturbative_lorentzian_quantum-gravity.pdf;sequence=1

Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change

Non-commutative Yang–Mills in IIB matrix model

We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite $N$ to all orders of the perturbation theory. Space-time is shown to be inseparable and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure the vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.

/pdf/space-time-structures-from-iib-matrix-model-vap3m2pckc.pdf

Space-time structures from iib matrix model

We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.

Noncommutative Yang-Mills in IIB Matrix Model

IIB Matrix Model

It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences---which can always be absorbed into a position of the critical surface---should be simply subtracted in model constructions. Such a picture gives another justification to the argument [W. A. Bardeen, Report No. FERMILAB-CONF-95-391-T] that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.

Hajime Aoki

Papers

Non-commutative Yang–Mills in IIB matrix model

Space-time structures from iib matrix model

Noncommutative Yang-Mills in IIB Matrix Model

IIB Matrix Model

Revisiting the naturalness problem: Who is afraid of quadratic divergences?