We present a holographic dual of four-dimensional, large N_c QCD with massless flavors. This model is constructed by placing N_f probe D8-branes into a D4 background, where supersymmetry is completely broken. The chiral symmetry breaking in QCD is manifested as a smooth interpolation of D8 - anti-D8 pairs in the supergravity background. The meson spectrum is examined by analyzing a five-dimensional Yang-Mills theory that originates from the non-Abelian DBI action of the probe D8-brane. It is found that our model yields massless pions, which are identified with Nambu-Goldstone bosons associated with the chiral symmetry breaking. We obtain the low-energy effective action of the pion field and show that it contains the usual kinetic term of the chiral Lagrangian and the Skyrme term. A brane configuration that defines a dynamical baryon is identified with the Skyrmion. We also derive the effective action including the lightest vector meson. Our model is closely related to that in the hidden local symmetry approach, and we obtain a Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation among the couplings. Furthermore, we investigate the Chern-Simons term on the probe brane and show that it leads to the Wess-Zumino-Witten term. The mass of the \eta' meson is also considered, and we formulate a simple derivation of the \eta' mass term satisfying the Witten-Veneziano formula from supergravity.

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Low energy hadron physics in holographic QCD

We investigate the behavior under SU3×SU3 of the hadron energy density and the closely related question of how the divergences of the axial-vector currents and the strangeness-changing vector currents transform under SU3×SU3. We assume that two terms in the energy density break SU3×SU3 symmetry; under SU3 one transforms as a singlet, the other as the member of an octet. The simplest possible behavior of these terms under chiral transformations is proposed: They are assigned to a single (3,3*)+(3*,3) representation of SU3×SU3 and parity together with the current divergences. The commutators of charges and current divergences are derived in terms of a single constant c that describes the strength of the SU3-breaking term relative to the chiral symmetry-breaking term. The constant c is found not to be small, as suggested earlier, but instead close to the value (-sqrt[2]) corresponding to an SU2×SU2 symmetry, realized mainly by massless pions rather than parity doubling. Some applications of the proposed commutation relations are given, mainly to the pseudoscalar mesons, and other applications are indicated.

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Behavior of Current Divergences under SU 3 × SU 3

Two sum rules are derived, relating moments of the spectral functions of the vector and axial-vector currents. If it is assumed that the $\ensuremath{\rho}$ and $A1$ mesons dominate these moments, then their masses must be in the ratio $\frac{{m}_{A1}}{{m}_{\ensuremath{\rho}}}=\sqrt{2}$, in very good agreement with experiment.

Precise Relations between the Spectra of Vector and Axial-Vector Mesons

Nonlinear Realization and Hidden Local Symmetries

Consequences of the local commutation relations of vector and axial currents proposed by Gell-Mann are explored: (1) A recipe for detecting and isolating Schwinger terms in the commutators, proportional to derivatives of the δ function, is discussed. (2) Under assumptions of smooth asymptotic behavior of form factors for forward scattering of the isovector current from a proton, we show that the U(3)⊗U(3) algebra for the time components of the currents implies the U(6)⊗U(6) algebra for space components, at least for spin-averaged diagonal single-particle states. (3) The derivation of the Adler-Weisberger formula for GAGV is sharpened by giving arguments that, at fixed energy, the forward π−p Green's function satisfies an unsubtracted dispersion relation in the pion mass. (4) A lower bound for inelastic electron-nucleon scattering at high momentum transfer is derived on the basis of U(6)⊗U(6). (5) The contribution of very virtual photons to the hyperfine anomaly in hydrogen is shown to be related to an equal-time commutator of currents; this contribution is crudely estimated to be <4 parts per million (ppm). (6) The logarithmically divergent part of electromagnetic mass differences of hadrons is shown to be proportional to matrix elements of the equal-time commutator of the electromagnetic current with its time derivative. It is suggested that this "divergent" part be identified with the Coleman-Glashow "tadpoles"; this suggestion is discussed in the framework of a simple quark model. (7) The logarithmically divergent part of the electromagnetic correction to the process π−→π0+e−+ν¯ is, on the basis of the U(6)⊗U(6) current algebra, shown to be nonvanishing, and is computed. (8) A speculative argument is presented that the rate e++e−→hadrons is comparable to the rate e++e−→μ++μ− in the limit of large energies.

http://inspirehep.net/record/49843/files/slac-pub-0165.pdf

Applications of the Chiral U ( 6 ) ⊗ U ( 6 ) Algebra of Current Densities

The notion of a partially conserved axial-vector current (1) (PCAC) and the current commutation relations that generate the algebra U(2)xU(2) have been successfully applied to the calculation of the axial-vector constant renormalization (2) and to the nonleptonic decays of hyperons and K mesons. (3) In this note, we wish to report on further applications of these ideas to the decays of vector mesons.

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Partially conserved axial vector current and the decays of vector mesons

In the theory of the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ group for baryons and mesons, there exist eighteen scalar and pseudoscalar densities. Confining ourselves to the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ subgroup, the pseudoscalar densities are equal to the divergences of the axial-vector currents and therefore can be interpreted as being proportional to the pion field on the basis of the partially-conserved-axial-vector-current hypothesis. An attempt is made to give physical interpretation to the scalar density by calculating the expectation value of its space integral with respect to nucleon states. It is found that this expectation value is small (at most, of the order of the pion mass), which is related to Adler's consistency condition on the pion-nucleon scattering amplitude implied by the PCAC hypothesis. Specific models that are consistent with the PCAC hypothesis, such as the gradient-coupling model and the \ensuremath{\sigma}-meson model, are examined on the basis of our result.

Scalar Densities in Current Commutation Relations and the Partially-Conserved-Axial-Vector-Current Hypothesis

Sum Rules for Magnetic Moments from Commutation Relations between Current Densities

Working with the equal-time commutation relations of vector current densities including the Schwinger term, the low-energy theorems for the Compton scattering of isovector photons by nucleons have been obtained. Assuming unsubtracted dispersion relations, sum rules which have been previously obtained by several authors have been reproduced and the relations between the previous derivations and the present work are discussed.

Exact Sum Rules as Consequences of Low-Energy Theorems and Unsubtracted Dispersion Relations

It is pointed out that within the quark model the equal-time commutation relations of currents provide us with a test of minimal electromagnetic interaction of the hadrons. When compared with experiment, the modifications of the Cabibbo-Radicati and Drell-Hearn sum rules resulting from nonminimal interactions may possibly fix the magnitudes of the isoscalar and the isovector Pauli interactions.

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Ken Kawarabayashi

Papers

Partially conserved axial vector current and the decays of vector mesons

Scalar Densities in Current Commutation Relations and the Partially-Conserved-Axial-Vector-Current Hypothesis

Sum Rules for Magnetic Moments from Commutation Relations between Current Densities

Exact Sum Rules as Consequences of Low-Energy Theorems and Unsubtracted Dispersion Relations

Minimal electromagnetic currents and commutation relations.