Anomaly Cancellations in the Type I D9-anti-D9 System and the USp(32) String Theory

We check some consistency conditions for the D9-anti-D9 system in type I string theory. The gravitational anomaly and gauge anomaly for SO(n) x SO(m) gauge symmetry are shown to be cancelled when n-m=32. In addition, we find that a string theory with USp(n) x USp(m) gauge symmetry also satisfies the anomaly cancellation conditions. After tachyon condensation, the theory reduces to a tachyon-free USp(32) string theory, though there is no spacetime supersymmetry.Comment: 17 pages + 10 eps figures, LaTeX; minor corrections, reference added, version to appear in Prog. Theor. Phy

Comments on Duality in MQCD

We clarify some ambiguous points in a derivation of duality via brane exchange using M-theory language, and propose a ``proof'' of duality in MQCD. Actually, duality in MQCD is rather trivial and does not need a complicated proof. The problem is how to interpret it in field theory language. We examine BPS states in N=2 theory and find the particle correspondence under duality. In the process, we also find some exotic particles in N=2 MQCD, and we observe an interesting phenomenon in type IIA string theory, namely, that fundamental strings are converted into D2-branes via the exchange of two NS5-branes. We also discuss how we should understand Seiberg's N=1 duality from exact duality in MQCD.Comment: 29 pages + 20 uuencoded eps figures, LaTeX with PTPTeXsty, typo corrected, version to appear in Prog. Theor. Phy

Mesons as Open Strings in a Holographic Dual of QCD

We study meson spectrum obtained from massive open string modes in a holographic dual of QCD constructed on the basis of a D4/D8-brane configuration in type IIA string theory. The spectrum includes mesons with spin higher than one. Taking into account the effect of curved background perturbatively, we obtain a mass formula for these mesons, which exhibits the linear Regge behavior at the leading order with subleading non-linear corrections. We argue that the string spectrum captures some features of the observed meson spectrum. For example, a_2(1320), b_1(1235), \pi(1300), a_0(1450), etc., are identified as the first excited massive open string states and \rho_3(1690), \pi_2(1670), etc., are identified as the second excited states.Comment: 26 pages, 2 figures, v2: references added, v3: published versio

Confinement and Dynamical Symmetry Breaking in non-SUSY Gauge Theory from S-duality in String Theory

We discuss an attempt to understand confinement and dynamical symmetry breaking in a 4-dimensional non-supersymmetric gauge theory using S-duality in type IIB string theory. The electric theory is a USp(2n) gauge theory and its magnetic dual is argued to be an SO(2n) or SO(2n-1) gauge theory. These theories are obtained as the low-energy effective theory of O3-D3bar systems in type IIB string theory, which are related by S-duality. Confinement and dynamical symmetry breaking in the USp(2n) gauge theory are caused by the condensation of scalar fields in the magnetic dual description, which is consistent with the scenario of the dual Meissner mechanism for the confinement.Comment: 41 pages, v2: minor corrections, version published in PT

Anomaly and superconnection

We study anomalies of fermions with spacetime-dependent mass. Using Fujikawa’s method, it is found that the anomalies associated with the U(N)+ × U(N)− chiral symmetry and U(N) flavor symmetry for even and odd dimensions, respectively, can be written in terms of superconnections. In particular, the anomaly for a vector-like U(1) symmetry is given by the Chern character of the superconnection in both even- and odd-dimensional cases. It is also argued that the non-Abelian anomaly for a system in D-dimensional spacetime is characterized by a (D + 2)-form part of the Chern character of the superconnection which generalizes the usual anomaly polynomial for the massless case. These results enable us to analyze anomalies in the systems with interfaces and spacetime boundaries in a unified way. Applications to index theorems, including the Atiyah–Patodi–Singer index theorem and a Callias-type index theorem, are also discussed. In addition, we give a natural string theory interpretation of these results

Holographic Chern-Simons Defects

We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD.Comment: 56 pages, 19 figures, v2: sign convention for CS level in terms of number of D7 branes switched, UV behavior of one and two point functions added in sec. 5.4.1 and 5.4.3, references added, typos correcte

Chern-Simons five-form and holographic baryons

In the top-down holographic model of QCD based on D4/D8-branes in type IIA string theory and some of the bottom-up models, the low energy effective theory of mesons is described by a five-dimensional Yang-Mills-Chern-Simons theory in a certain curved background with two boundaries. The five-dimensional Chern-Simons term plays a crucial role in reproducing the correct chiral anomaly in four-dimensional massless QCD. However, there are some subtle ambiguities in the definition of the Chern-Simons term for the cases with topologically nontrivial gauge bundles, which include the configurations with baryons. In particular, for the cases with three flavors, it was pointed out by Hata and Murata that the naive Chern-Simons term does not lead to an important constraint on the baryon spectrum, which is needed to pick out the correct baryon spectrum observed in nature. In this paper, we propose a formulation of a well-defined Chern-Simons term which can be used for the cases with baryons, and show that it recovers the correct baryon constraint as well as the chiral anomaly in QCD.Japan Society for the Promotion of Science (International Research Fellow)Croucher FellowshipJapan Society for the Promotion of Science. Grant-in-Aid for Scientific Research (Grant No. JP16K05324