Chong-Sun Chu

Constrained quantization of open string in background B field and noncommutative D-brane

In a previous paper we provided a consistent quantization of open strings ending on D-branes with a background B field. In this letter, we show that the same result can also be obtained using the more traditional method of Diracs constrained quantization. We also extend the discussion to the fermionic sector.

SUSY breaking by a metastable ground state: why the early Universe preferred the non-supersymmetric vacuum

Supersymmetry breaking in a metastable vacuum is re-examined in a cosmological context. It is shown that thermal effects generically drive the Universe to the metastable minimum even if it begins in the supersymmetry-preserving one. This is a generic feature of the ISS models of metastable supersymmetry breaking due to the fact that SUSY preserving vacua contain fewer light degrees of freedom than the metastable ground state at the origin. These models of metastable SUSY breaking are thus placed on an equal footing with the more usual dynamical SUSY breaking scenarios.

Towards the quantum geometry of the M5-brane in a constant C-field from multiple membranes

We show that the Nahm equation which describes a fuzzy D3-brane in the presence of a B-field can be derived as a boundary condition of the F1-strings ending on the D3-brane, and that the modifications of the original Nahm equation by a B-field can be understood in terms of the noncommutative geometry of the D3-brane. Naturally this is consistent with the alternative derivation by quantising the open strings in the B-field background. We then consider a configuration of multiple M2-branes ending on an M5-brane with a constant 3-form C-field. By analogy with the case of strings ending on a D3-brane with a constant B-field, one can expect that this system can be described in terms of the boundary of the M2-branes moving within a certain kind of quantum geometry on the M5-brane worldvolume. By repeating our analysis, we show that the analogue of the B-field modified Nahm equation, the C-field modified Basu-Harvey equation can also be understood as a boundary condition of the M2-branes. We then compare this to the M5-brane BIon description and show that the two descriptions match provided we postulate a new type of quantum geometry on the M5-brane worldvolume. Unlike the D-brane case, this is naturally expressed in terms of a relation between a 3-bracket of the M5-brane worldvolume coordinates and the C-field.

Noncommutative D-brane and open string in pp wave background with B field

The open string ending on a D-brane with a constant B-field in a pp-wave Ramond–Ramond background is exactly solvable. The theory is controlled by three dimensionful parameters: α′, the mass parameter (RR background times the lightcone momentum) and the B-field. We quantize the open string theory and determine the full noncommutative structure. In particular, we find a fully noncommutative phase space whose noncommutativity depends on all these parameters. The lightcone Hamiltonian is obtained, and as a consequence of the nontrivial commutation relations of the theory, new features of the spectrum are noted. Various scaling limits of the string results are considered. Physical implications are discussed.

Time-dependent AdS/CFT duality and null singularity

We consider AdS/CFT correspondence for time-dependent II B backgrounds in this paper. The supergravity solutions we construct are supersymmetric pp-waves on AdS and may have null singularity in the bulk. The dual gauge theory is also constructed explicitly and is given by a time-dependent supersymmetric Yang-Mills theory living on the boundary. Apart from the usual terms that are dictated by the geometry, our gauge theory action features also a time-dependent axion coupling and a time-dependent gauge coupling. Both of which are necessary due to the presence of a nontrivial dilaton and axion profile in the supergravity solution. The proposal is supported by a precise matching in the symmetries and functional dependence on the null coordinate of the two theories. As applications, we show how the bulk Einstein equation may be reproduced from the gauge theory. We also study and compare the behaviour of the field theory two-point functions. We find that the two-point function computed by using duality is different from that by doing a direct field theory computation. In particular the spacetime singularity is not seen in our gauge theory result, suggesting that the spacetime singularity may be resolved in the gauge theory.

A note on string interaction on the pp-wave background

We consider type IIB string interaction on the maximally supersymmetric pp-wave background and discuss how the bosonic symmetries of the background are realized. This analysis shows that there are some interesting differences with respect to the flat-space case and suggests modifications to the existing form of the string vertex. We focus on the zero-mode part which is responsible for some puzzling string predictions about the super Yang–Mills side. We show that these puzzles disappear when a symmetry preserving string interaction is used.

Magnons, classical strings and β-deformations

Motivated by the recent work of Hofman and Maldacena [1] we construct a classical string solution on the β-deformed AdS5 × 5 background. This string solution is identified with a magnon state of the integrable spin chain description of the = 1 supersymmetric β-deformed gauge theory. The string solution carries two angular momenta, an infinite J1 and a finite J2 which classically can take arbitrary values. This string solution corresponds to the magnon of charge J2 propagating on an infinite spin chain. We derive an exact dispersion relation for this magnon from string theory.

String theory and noncommutative field theories at one loop

By exploiting the boundary state formalism we obtain the string correlator between two internal points on the one loop open string world-sheet in the presence of a constant background B-field. From this derivation it is clear that there is an ambiguity when one tries to restrict the Green function to the boundary of the surface. We fix this ambiguity by showing that there is a unique form for the correlator between two points on the boundary which reproduces the one loop field theory results of different noncommutative field theories. In particular, we present the derivation of one loop diagrams for φ36 and φ44 scalar interactions and for Yang–Mills theory. From the 2-point function we are able to derive the one loop β-function for noncommutative gauge theory.

Notes on noncommutative instantons

Abstract We study in detail the ADHM construction of U ( N ) instantons on noncommutative Euclidean space–time R NC 4 and noncommutative space R NC 2 × R 2 . We point out that the completeness condition in the ADHM construction could be invalidated in certain circumstances. When this happens, regular instanton configuration may not exist even if the ADHM constraints are satisfied. Some of the existing solutions in the literature indeed violate the completeness condition and hence are not correct. We present alternative solutions for these cases. In particular, we show for the first time how to construct explicitly regular U ( N ) instanton solutions on R NC 4 and on R NC 2 × R 2 . We also give a simple general argument based on the Corrigans identity that the topological charge of noncommutative regular instantons is always an integer.

Hermitian analyticity, IR / UV mixing and unitarity of noncommutative field theories

The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established in an explicit form. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. These unitarity constraints relate the discontinuities of amplitudes with physical intermediate states and allow us to see how the IR/UV mixing may lead to a breakdown of unitarity. Specifically, we show that the IR/UV singularity does not lead to the violation of unitarity in the space–space noncommutative case, but it does lead to its violation in a space–time noncommutative field theory. As a corollary, noncommutative field theory without IR/UV mixing will be unitary in both the space–space and space–time noncommutative case. To illustrate this, we introduce and analyse the noncommutative Lee model—an exactly solvable quantum field theory. We show that the model is free from the IR/UV mixing in both the space–space and space–time noncommutative cases. Our analysis is exact. Due to absence of the IR/UV mixing one can expect that the theory is unitary. We present some checks supporting this claim. Our analysis provides a counter example to the generally held belief that field theories with space–time noncommutativity are nonunitary.