We revisit local mirror symmetry associated with del Pezzo surfaces in CalabiYau threefolds in view of five-dimensional N =1 E N theories compactified on a circle. The mirror partner of singular Calabi-Yau with a shrinking del Pezzo four-cycle is described as the affine 7-brane backgrounds probed by a D3-brane. Evaluating the mirror map and the BPS central charge we relate junction charges to RR charges of D-branes wrapped on del Pezzo surfaces. This enables us to determine how the string junctions are mapped to D-branes on del Pezzo surfaces.

We consider the noncommutative deformation of the Sakai-Sugimoto model at finite temperature and finite baryon chemical potential. The space noncommutativity is possible to have an influence on the flavor dynamics of the QCD. The critical temperature and critical value of the chemical potential are modified by the space noncommutativity. The influence of the space noncommutativity on the flavor dynamics of the QCD is caused by the Wess-Zumino term in the effective action of the D8-branes. The intermediate temperature phase, in which the gluons deconfine but the chiral symmetry remains broken, is easy to be realized in some region of the noncommutativity parameter.

We study the BPS spectrum of four-dimensional N = 2 SU(2) theory with massive fundamental matter fields using the D3-brane probe. Since the BPS states are realized by string webs subject to the BPS conditions, we determine explicitly the configurations of such webs. It is observed that there appear BPS string webs with multiple junctions corresponding to the fact that the curves of marginal stability in the massive theory are infinitely nested. In terms of the string configurations, various properties of the curves of marginal stability are described intuitively. §2. SU (2) theory with N = 1 massless matter fieldWe begin with SU (2) theory with N f = 1 massless matter field. Denoting by z the order parameter of the Coulomb branch, it was shown that the theory has three singularities at z = z i (i = 1, 2, 3) in the moduli space, where a dyon (or monopole) with electric-magnetic charges (p i , q i ) becomes massless. In the type IIB * )

We have constructed a noncommutative deformation of the holographic QCD (Sakai-Sugimoto) model and evaluated the mass spectrum of low spin vector mesons at finite temperature. The masses of light vector-and pseudovector-meson in the noncommutative holographic QCD model reduces over the whole area in the intermediate-temperature regime compared to the commutative case. However, the space noncommutativity does not change the properties of temperature dependence for the mass spectrum of low spin mesons. The masses of meson also decrease with increasing temperature in noncommutative case.

We investigate the Kaluza-Klein (KK) spectrum of N = 1 supersymmetric gauge theory compactified on a circle. We concentrate on a model with gauge group SU (2) and four massless matter fields in the fundamental representation. We derive the exact mass formula of KK modes by using Seiberg-Witten theory. From the mass formula and the D3-brane probe realization, we determine the spectrum of KK modes of matter fields and gauge fields. As a result, we find that the lightest KK state of gauge fields is stable for all the vacuum moduli space, while the lightest KK state of matter fields decays easier than other KK states in a region of the moduli space. The region becomes small as we decrease the five-dimensional gauge coupling constant g 5 , and vanishes as we take the limit g 5 → 0. This result continuously connects the known KK spectrum in the weak coupling limit and that in the strong coupling limit.