Akitsugu Miwa

Holography of Wilson-loop expectation values with local operator insertions

We study the expectation values of Wilson-loop operators with the insertions of local operators ZJ and J for large J from the bulk viewpoint of AdS/CFT correspondence. Classical solutions of strings attached to such deformed Wilson loops at the conformal boundary are constructed and are applied to the computation of Wilson-loop expectation values. We argue that in order to have such solutions for general insertions at finite positions in the base spacetime of the gauge theory, it is crucial to interpret the holographic correspondence in the semi-classical picture as a tunneling phenomenon, as has been previously established for holographic computations of correlators of BMN operators. This also requires to use the Euclideanized AdS background and Euclidean super Yang-Mills theory.

Holographic QCD and pion mass

To realize massive pions, we study variations of the holographic model of massless QCD using the D4/D8/ brane configuration proposed by Sakai and Sugimoto. We propose deformations which break the chiral symmetry explicitly and compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. We also argue a chiral perturbation corresponding to our deformation.

Effects of space-time noncommutativity on the angular power spectrum of the CMB

Abstract We investigate an inflationary model of the universe based on the assumption that space–time is noncommutative in the very early universe. We analyze the effects of space–time noncommutativity on the quantum fluctuations of an inflaton field and investigate their contributions to the cosmic microwave background (CMB). We show that the angular power spectrum l ( l +1) C l generically has a sharp damping for lower l if we assume that the last scattering surface is traced back to fuzzy spheres at the times when large-scale modes cross the Hubble horizon.

Boundary condition for a D-brane from the wilson loop, and gravitational interpretation of an eigenvalue in the matrix model in ADS/CFT correspondence

We study the supersymmetric Wilson loops in the four-dimensional N=4 super Yang-Mills theory in the context of AdS/CFT correspondence. In the gauge theory side, it is known that the expectation value of the Wilson loops of circular shape with winding number k, W{sub k}(C), is calculable by using a Gaussian matrix model. In the gravity side, the expectation value of the loop is conjectured to be given by the classical value of the action S{sub D3} for a probe D3-brane with k electric fluxes as =e{sup -S{sub D3}}. Given such correspondence, we pursue the interpretation of the matrix model eigenvalue density, or more precisely the resolvent, from the viewpoint of the probe D3-brane. We see that the position of an eigenvalue appears as the gauge field plus the scalar field integrated over the boundary of the probe D3-brane. In the course of our analysis, we also clarify the boundary condition on the D3-brane in terms of the Wilson loop.

Chiral magnetic effect from Q-balls

We apply a generic framework of linear sigma models for revealing a mechanism of the mysterious phenomenon, the chiral magnetic effect, in quark-gluon plasma. An electric current arises along a background magnetic field, which is given rise to by Q-balls (non-topological solitons) of the linear sigma model with axial anomaly. We find additional alternating current due to quark mass terms. The hadronic Q-balls, baby boson stars, may be created in heavy-ion collisions.

A Mechanism of the large scale damping in the CMB anisotropy

Abstract We present a mechanism through which a certain class of short-distance cutoff affects the CMB anisotropies at large angular scales. Our analysis is performed in two steps. The first is given in an intuitive way, using the property of the inflationary universe that quantum fluctuations of an inflaton field become classical after crossing the Hubble horizon. We give a condition for a cutoff to yield a damping on large scales, and show that the holographic cutoff introduced in the preceding paper ( hep-th/0307029 ) does satisfy the condition. The second analysis is carried out by setting an initial condition such that each mode of inflaton starts as the vacuum fluctuation of the Hamiltonian when being released from the constraint of cutoff. The first intuitive discussion is then shown to be correct qualitatively.

Deformation of half-BPS solution in ABJM model and instability of supermembrane

It is well-known that a supermembrane in the light-cone gauge has a continuous spectrum and is unstable. Physical interpretation of this instability is that a supermembrane can have a long thin tube without cost of energy and consequently it becomes a spiky configuration in which multiple membranes are connected by thin tubes.On the other hand, the ABJM model was proposed as a low-energy description of multiple M2-branes in the static gauge. It is natural that an M2-brane is also unstable in this gauge if we believe the physical picture in the light-cone gauge. In order to examine this, we construct a BPS solution explicitly both in the Nambu-Goto action of a supermembrane in the static gauge and in the U(1) × U(1) ABJM model, which represents intersecting M2-branes. Since this configuration is regarded as a single M2-brane emitting another one, we study the instability of an M2-brane by analyzing fluctuations around it. We show that a zero mode exists which can deform the configuration. For comparison, we also examine a similar configuration on the D2-brane and check that it does not have such zero modes under a fixed string charge. Furthermore we confirm that the novel Higgs mechanism translates our BPS solution in the ABJM model into that in the D2-brane world volume theory, where the winding number of the former around the fixed point of the orbifold becomes the number of strings ending on the D2-brane in the latter.

Loop equation in D=4, N=4 super Yang-Mills theory and string field equation on AdS{sub 5}xS{sup 5}

We consider the loop equation in four-dimensional N=4 SYM, which is a functional differential equation for the Wilson loop W(C) and expresses the propagation and the interaction of the string C. Our W(C) consists of the scalar and the gaugino fields as well as the gauge field. The loop C is specified by six bosonic coordinates y^i(s) and two fermionic coordinates \zeta(s) and \eta(s) besides the four-dimensional spacetime coordinates x^\mu(s). We have successfully determined, to quadratic order in \zeta and \eta, the parameters in W(C) and the loop differential operator so that the equation of motion of SYM can be correctly reproduced to give the non-linear term of W(C). We extract the most singular and linear part of our loop equation and compare it with the Hamiltonian constraint of the string propagating on AdS_5 \times S^5 background.

Noncommutative inflation and the large scale damping in the CMB anisotropy

We show that a certain class of short-distance cutoff can give rise to large suppression on the CMB anisotropies at large angular scales.

A tunneling picture of dual giant Wilson loop

We further discuss a rotating dual giant Wilson loop (D3-brane) solution constructed in Lorentzian AdS by Drukker et al. The solution is shown to be composed of a dual giant Wilson loop and a dual giant graviton by minutely examining its shape. Hence it may be supposed that the dual gauge-theory operator should be a k-th symmetric Wilson loop with insertions of dual giant graviton operators. To give a convincing argument for this observation, the classical action of the solution should be evaluated in Euclidean signature. For this purpose we perform a Wick rotation to the Lorentzian solution by following the tunneling prescription and obtain Euclidean solutions attaching to a circle or a straight line on the AdS boundary. The classical action contains a logarithmic divergence which is proportional to the R-charge. It is consistent with the correlation function of the dual giant graviton operators. Because of ambiguities concerning regularization, finite terms of the action do not lead to conclusive evidence. However we may expect that the ambiguities would cancel by subtracting the action of the D3-brane with a straight-line boundary from that with a circular boundary. It is really shown that the difference is consistent with the expectation value of the k-th symmetric Wilson loop. Although our analysis does not specify the unique dual gauge-theory operator, we discuss possible candidates implied by the D3-brane computation.