Yuya Sasai

Braided Quantum Field Theories and Their Symmetries

Braided quantum field theories, proposed by Oeckl, can provide a framework for quantum field theories that possess Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We study Hopf algebra symmetries and such relations in the context of braided quantum field theories. We give the four algebraic conditions among Hopf algebra symmetries and braided quantum field theories that are required for the relations to hold. As concrete examples, we apply our

One-loop unitarity of scalar field theories on Poincaré invariant commutative nonassociative spacetimes

We study scalar field theories on Poincare invariant commutative nonassociative spacetimes. We compute the one-loop self-energy diagrams in the ordinary path integral quantization scheme with Feynmans prescription, and find that the Cutkosky rule is satisfied. This property is in contrast with that of noncommutative field theory, since it is known that noncommutative field theory with space/time noncommutativity violates unitarity in the above standard scheme, and the quantization procedure will necessarily become complicated to obtain a sensible Poincare invariant noncommutative field theory. We point out a peculiar feature of the non-locality in our nonassociative field theories, which may explain the property of the unitarity distinct from noncommutative field theories. Thus commutative nonassociative field theories seem to contain physically interesting field theories on deformed spacetimes.

Exact results in quiver quantum mechanics and BPS bound state counting

A bstractWe exactly evaluate the partition function (index) of N

The Cutkosky Rule of Three Dimensional Noncommutative Field Theory in Lie Algebraic Noncommutative Spacetime

\mathcal{N}

Closed string transport coefficients and the membrane paradigm

= 4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained by solving the BRST equations, and D-term and F-term conditions. We turn on background gauge fields of R-symmetries for the chiral multiplets corresponding to the arrows between quiver nodes, but the partition function does not depend on these R-charges. We give explicit examples of the quiver theory including a non-coprime dimension vector. The partition functions completely agree with the mathematical formulæ of the Poincaré polynomials (χy-genus) and the wall crossing for the quiver moduli spaces. We also discuss exact computation of the expectation values of supersymmetric (Q-closed) Wilson loops in the quiver theory.

Compressible fluids in the membrane paradigm: Non-AdS fluid/gravity correspondences

Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar

Transport coefficients of D1-D5-P system and the membrane paradigm

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DOMAIN WALL SOLITONS AND HOPF ALGEBRAIC TRANSLATIONAL SYMMETRIES IN NONCOMMUTATIVE FIELD THEORIES

braided noncommutative field theory in Lie-algebraic noncommutative space-time,