Anomalies and Tadpoles in Open/Closed String Duality

We discuss the role played by the divergences appearing in the interaction between a fractional D3 brane dressed with an SU(N) gauge field and a stack of N fractional D3 branes on the orbifolds C^2/Z_2 and C^3/(Z_2 x Z_2). In particular we show that the logarithmic divergences in the closed string channel, interpreted as due to twisted massless tadpoles, are mapped, under open/closed string duality, in the logarithmic ones in the open string channel, due to the massless states circulating in the annulus diagram and corresponding to the one-loop divergences that one finds in the gauge theory living in the world volume of the brane. This result provides a quantitative evidence of why the chiral and scale anomalies of the supersymmetric and non conformal gauge theories supported by the world volume of the branes can be inferred from supergravity calculations.Comment: LaTeX, 8 pages. Contribution to the proceedings of the workshop of the RTN Network "The quantum structure of space-time and the geometric nature of fundamental interactions", Copenhagen, September 200

On CP-Odd Effects in K_L \to 2\pi and K^{\pm} \to \pi^{\pm} \pi^{\pm} \pi^{\mp} Decays Generated by Direct CP Violation

The amplitudes of the K^{\pm} \to 3\pi and K \to 2\pi decays are expressed in terms of different combinations of one and the same set of CP-conserving and CP-odd parameters. Extracting the magnitudes of these parameters from the data on K \to 2\pi decays, we estimate an expected CP-odd difference between the values of the slope parameters g^+ and g^- of the energy distributions of "odd" pions in K^+ \to \pi^+\pi^+\pi^- and K^- \to \pi^-\pi^-\pi^+ decays.Comment: 12 pages, no figure

N=1 Matter from Fractional Branes

We study a bound state of fractional D3-branes localized inside the world-volume of fractional D7-branes on the orbifold C^3/Z_2 x Z_2. We determine the open string spectrum that leads to N=1 U(N1)xU(N2)xU(N3)xU(N4) gauge theory with matter having the number of D7-branes as a flavor index. We derive the linearized boundary action of the D7-brane on this orbifold using the boundary state formalism and we discuss the tadpole cancellation. After computing the asymptotic expression of the supergravity solution the anomalies of the gauge theory are reproduced.Comment: LaTeX 20 pages, 1 figure, small changes and references adde

On the Gauge/Gravity Correspondence and the Open/Closed String Duality

In this article we review the conditions for the validity of the gauge/gravity correspondence in both supersymmetric and non-supersymmetric string models. We start by reminding what happens in type IIB theory on the orbifolds C^2/Z_2 and C^3/(Z_2 x Z_2), where this correspondence beautifully works. In these cases, by performing a complete stringy calculation of the interaction among D3 branes, it has been shown that the fact that this correspondence works is a consequence of the open/closed duality and of the absence of threshold corrections. Then we review the construction of type 0 theories with their orbifolds and orientifolds having spectra free from both open and closed string tachyons and for such models we study the validity of the gauge/gravity correspondence, concluding that this is not a peculiarity of supersymmetric theories, but it may work also for non-supersymmetric models. Also in these cases, when it works, it is again a consequence of the open/closed string duality and of vanishing threshold corrections.Comment: Invited review article for Int. J. Mod. Phys. A, 95 pages, 2 figures, 3 tables, LaTeX. References and acknowledgements adde

The b→sγγb\to s\gamma\gamma transition in softly broken supersymmetry

We study the effect of supersymmetric contributions to the effective quark transition $b\to s\gamma\gamma$, including leading order QCD effects. We apply the discussion to the decay $B_s\to\gamma\gamma$. Even though one-particle irreducible contributions could play a role, numerical cancelations make the amplitude for the two-photon emission strongly correlated to the $b\to s\gamma$ amplitude which is sharply constrained by experiment. A quite general statement follows: as long as non-standard physics effects appear only in the matching of the Wilson coefficients of the standard effective operator basis, the deviations from the standard model expectations of the decay rates induced by $b\to s\gamma\gamma$ are bound to follow closely the corresponding deviations on $b\to s\gamma$. Effects of new physics are therefore bound to be small.Comment: Latex2e, RevTex, 22 pages, 8 eps figures, comments and references adde

New checks and subtleties for AdS/CFT and a-maximization

We provide a cross-check of AdS/CFT and a-charge maximization for a four dimensional $N$=1 SCFT with irrational R-charges. The gauge theory is the low energy effective theory of N D3-branes at the tip of the complex cone over the first del Pezzo surface. By carefully taking into account the subtle issue of flavor symmetry breaking at the fixed point, we show, using a-maximization, that this theory has in fact irrational central charge and R-charges. Our results perfectly match with those inherited from the recently discovered supergravity dual background. Along analogous lines, we make novel predictions for the still unknown AdS dual of the quiver theory for the second del Pezzo surface. This should flow to a SCFT with irrational charges, too. All of our results differ from previous findings in the literature and outline interesting subtleties in a-maximization and AdS/CFT techniques overlooked in the past.Comment: Latex, 16 pagex, 2 figures; v2, comments and a reference added; v3, typos correcte

Feynman Rules in the Type III Natural Flavour-Conserving Two-Higgs Doublet Model

We consider a two Higgs-doublet model with $S_3$ symmetry, which implies a $\pi \over 2$ rather than 0 relative phase between the vacuum expectation values $$and$$. The corresponding Feynman rules are derived accordingly and the transformation of the Higgs fields from the weak to the mass eigenstates includes not only an angle rotation but also a phase transformation. In this model, both doublets couple to the same type of fermions and the flavour-changing neutral currents are naturally suppressed. We also demonstrate that the Type III natural flavour-conserving model is valid at tree-level even when an explicit $S_3$ symmetry breaking perturbation is introduced to get a reasonable CKM matrix. In the special case $\beta = \alpha$, as the ratio $\tan\beta = {v_2 \over v_1}$ runs from 0 to $\infty$, the dominant Yukawa coupling will change from the first two generations to the third generation. In the Feynman rules, we also find that the charged Higgs currents are explicitly left-right asymmetric. The ratios between the left- and right-handed currents for the quarks in the same generations are estimated.Comment: 16 pages (figures not included), NCKU-HEP/93-1