Search

We consider large N zero-coupling d-dimensional U ( N ) gauge theories, with N f matter fields in the fundamental representation on a compact spatial manifold S d − 1 × time, with N f / N finite. The Gauss' law constraint induces interactions among the fields, in spite of the zero-coupling. This class of theories undergo a 3rd order deconfinement phase transition at a temperature T c proportional to the inverse length scale of the compact manifold. The low-temperature phase has a free-energy of O ( N f 2 ) , interpreted as that of a gas of (color singlet) mesons and glueballs. The high-temperature (deconfinement) phase has a free energy of order N 2 f ( N f / N , T ) , which is interpreted as that of a gas of gluons and of fundamental and anti-fundamental matter states. This suggests the existence of a dual string theory, and a transition to a black hole at high temperature.

We perform a completely perturbative matrix model calculation of the physical low-energy quantities of the N=2 U(N) gauge theory. Within the matrix model framework we propose a perturbative definition of the periods a_i in terms of certain tadpole diagrams, and check our conjecture up to first order in the gauge theory instanton expansion. The prescription does not require knowledge of the Seiberg-Witten differential or curve. We also compute the N=2 prepotential F(a) perturbatively up to the first-instanton level finding agreement with the known result.

We study the N=1 Sp(2N+2M)xSp(2N) cascading gauge theory on a stack of N physical and M fractional (half) D3-branes at the singularity of an orientifolded conifold. In addition to the D3-branes and an O7-plane, the background contains eight D7-branes, which give rise to matter in the fundamental representation of the gauge group. The moduli space of the gauge theory is analyzed and its structure is related to the brane configurations in the dual type IIB theory and in type IIA/M-theory.

The renormalization group flows of the coupling constants for the gauged U(N) vector model, with N_f massless fermions in the defining representation, are studied in the large N limit, to all orders in the scalar coupling lambda, leading order in 1/N, and lowest two orders in the gauge coupling g^2. It is shown that the restrictions of asymptotic freedom, and the reality of the coupling constants throughout the flows, places important restrictions on N_f/N. For the case with massless mesons, these conditions are sufficiently restrictive to imply the existence of an infrared fixed-point (g_*,lambda_*) in both couplings. Thus, the consistent massless theory is scale invariant, and in a non-abelian Coulomb phase. The case of massive mesons, and of spontaneously broken symmetry is also discussed, with similar, but not identical, conclusions. Speculations related to the possibility that there is a non-perturbative (in g^2) breakdown of chiral symmetry are presented., 15 pages, plain Latex, one figure added

A calculation of the renormalization group improved effective potential for the gauged U(N) vector model, coupled to $N_f$ fermions in the fundamental representation, computed to leading order in 1/N, all orders in the scalar self-coupling $\lambda$, and lowest order in gauge coupling $g^2$, with $N_f$ of order $N$, is presented. It is shown that the theory has two phases, one of which is asymptotically free, and the other not, where the asymptotically free phase occurs if $0 < \lambda /g^2 < {4/3} (\frac{N_f}{N} - 1)$, and $\frac{N_f}{N} < {11/2}$. In the asymptotically free phase, the effective potential behaves qualitatively like the tree-level potential. In the other phase, the theory exhibits all the difficulties of the ungauged $(g^2 = 0)$ vector model. Therefore the theory appears to be consistent (only) in the asymptotically free phase., Comment: Latex, 18 pages plus 3 figures using epsf. Substantially revised to correct a factor of 2 error in the previous version of equation (2.5b). This has significant effects on the results. The model has also been revised to include fermions

We examine the high energy (Regge) limit of gravitational scattering using a Wilson line approach previously used in the context of non-Abelian gauge theories. Our aim is to clarify the nature of the Reggeization of the graviton and the interplay between this Reggeization and the so-called eikonal phase which determines the spectrum of gravitational bound states. Furthermore, we discuss finite corrections to this picture. Our results are of relevance to various supergravity theories, and also help to clarify the relationship between gauge and gravity theories., 33 pages, 5 figures

We demonstrate that the large-N expansion of Wilson loop expectation values in SO(N) and Sp(N) Yang-Mills theory on orientable and nonorientable surfaces has a natural description as a weighted sum over covers of the given surface. The sum takes the form of the perturbative expansion of an open string theory. The derivation makes contact with the classification of branched covers by Gabai and Kazez. Comparison with the analogous results for the chiral sectors of QCD_2 is instructive for both cases., 24 pages, LaTeX, no figures, minor changes for published version

We extend the analysis of Higgs-regulated planar amplitudes of N=4 supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine). We also study various Regge limits of N=4 SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n \geq 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion.

We compute the three-loop contribution to the N=4 supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level. We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization., Comment: 45 pages, 9 figures; v3: major revision (more stringent tests, discussion of order of limits in the Regge regime)

Planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior, anticipated by the 't Hooft genus expansion and the $AdS/CFT$ correspondence. We examine the Bern-Dixon-Smirnov (BDS) conjecture for $n$-gluon amplitudes in the context of single-Regge and multi-Regge limits and show that these amplitudes have the expected Regge form in the Euclidean region., 48 pages, 8 figures; Noted added commenting on related work which appeared after the initial posting. References and clarifications added, as well as typos corrected

We present a matrix-model expression for the sum of instanton contributions to the prepotential of an N=2 supersymmetric U(N) gauge theory, with matter in various representations. This expression is derived by combining the renormalization-group approach to the gauge theory prepotential with matrix-model methods. This result can be evaluated order-by-order in matrix-model perturbation theory to obtain the instanton corrections to the prepotential. We also show, using this expression, that the one-instanton prepotential assumes a universal form., 20 pages, LaTeX, 2 figures

We study the matrix model/gauge theory connection for three different N=1 models: U(N) x U(N) with matter in bifundamental representations, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. Using Ward identities, we explicitly show that the loop equations of the matrix models lead to cubic algebraic curves. We then establish the equivalence of the matrix model and gauge theory descriptions in two ways. First, we derive generalized Konishi anomaly equations in the gauge theories, showing that they are identical to the matrix-model equations. Second, we use a perturbative superspace analysis to establish the relation between the gauge theories and the matrix models. We find that the gauge coupling matrix for U(N) with matter in the symmetric or antisymmetric representations is_not_ given by the second derivative of the matrix-model free energy. However, the matrix-model prescription can be modified to give the gauge coupling matrix., 27 pages, 2 figures; v2: minor corrections and clarifications; v3: published version

We analyze the large N supergravity descriptions of the class of type IIB models T-dual to elliptic type IIA brane configurations containing two orientifold 6-planes and up to two NS 5-branes. The T-dual IIB configurations contain N D3-branes in the background of an orientifold 7-plane and, in some models, a Z_2 orbifold and/or D7-branes, which give rise to four-dimensional N=2 (or N=4) gauge theories with at most two factors. We identify the chiral primary states of the supergravity theories, and match them to gauge invariant operators of the corresponding superconformal theories using Maldacena's duality., Comment: 44 pages (typo corrected)

We give a unified analysis of four-dimensional elliptic models with N=2 supersymmetry and a simple gauge group, and their relation to M-theory. Explicit calculations of the Seiberg-Witten curves and the resulting one-instanton prepotential are presented. The remarkable regularities that emerge are emphasized. In addition, we calculate the prepotential in the Coulomb phase of the (asymptotically-free) Sp(2N) gauge theory with N_f fundamental hypermultiplets of arbitrary mass., 52 pages, latex, one eps figure, uses psfig.tex; revised version: typos corrected and references added

The one-instanton contribution to the prepotential for N=2 supersymmetric gauge theories with classical groups exhibits a universality of form. We extrapolate the observed regularity to SU(N) gauge theory with two antisymmetric hypermultiplets and N_f \leq 3 hypermultiplets in the defining representation. Using methods developed for the instanton expansion of non-hyperelliptic curves, we construct an effective quartic Seiberg-Witten curve that generates this one-instanton prepotential. We then interpret this curve in terms of an M-theoretic picture involving NS 5-branes, D4-branes, D6-branes, and orientifold sixplanes, and show that for consistency, an infinite chain of 5-branes and orientifold sixplanes is required, corresponding to a curve of infinite order., Comment: 30 pages; 3 figures; LaTeX; minor typos corrected

We consider N=2 supersymmetric Yang-Mills theories in four dimensions with gauge group SU(N) for N larger than two. Using the cubic curve for a matter hypermultiplet transforming in the symmetric representation, obtained from M-theory by Landsteiner and Lopez, we calculate the prepotential up to the one instanton correction. We treat the curve to be approximately hyperelliptic and perform a perturbation expansion for the Seiberg-Witten differential to get the one instanton contribution. We find that it reproduces the correct result for one-loop, and we obtain the prediction for that curve for the one instanton correction term., Comment: 31 p., plain latex

We continue our analysis of the field strength correlation functions of two-dimensional QCD on Riemann surfaces by studying the large $N$ limit of these correlation functions on the sphere for gauge group $U(N)$. Our results allow us to exhibit an explicit master field for the field strength $F_{\mu\nu}$ in a ``topological gauge'', given by a single master matrix in the Lie algebra of the maximal torus of the gauge group. Field correlators are obtained from traces of products of the master field. We also obtain a master field for the gauge potential $A_{\mu}$ on the sphere, consistent with the master field for the field strength., Comment: 14 pages, latex file, no macros, 1 reference added

We exhibit the gauge-group independence (``universality'') of all normalized non-intersecting Wilson loop expectation values in the large N limit of two-dimensional Yang-Mills theory. This universality is most easily understood via the string theory reformulation of these gauge theories. By constructing an isomorphism between the string maps contributing to normalized Wilson loop expectation values in the different theories, we prove the large N universality of these observables on any surface. The string calculation of the Wilson loop expectation value on the sphere also leads to an indication of the large N phase transition separating strong- and weak-coupling phases., Comment: 18 pages, phyzzx macro, no figures

We derive a compact all-loop-order expression for the IR-divergent part of the N=4 SYM four-gluon amplitude, which includes both planar and all subleading-color contributions, based on the assumption that the higher-loop soft anomalous dimension matrices are proportional to the one-loop soft anomalous dimension matrix, as has been recently conjectured. We also consider the Regge limit of the four-gluon amplitude, and we present evidence that the leading logarithmic growth of the subleading-color amplitudes is less severe than that of the planar amplitudes. We examine possible 1/N^2 corrections to the gluon Regge trajectory, previously obtained in the planar limit from the BDS ansatz. The double-trace amplitudes have Regge behavior as well, with a nonsense-choosing Regge trajectory and a Regge cut which first emerges at three loops., 29 pages; v2: corrections to sections 5.1 and 5.2, references added; v3: clarification in introduction, references added; v4: published version

We use matrix model technology to study the N=2 U(N) gauge theory with N_f massive hypermultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods a_i and the prepotential F(a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve and differential from the large-M solution of the matrix model. We show that the two cases N_f, Comment: 22 pages, 2 figures; v3: added sec. 8, containing a derivation of the SW differential purely within the matrix model framework; references added

Meson hyperfine splittings give empirical evidence that the short-ranged part of the potential binding quarks has the behavior expected of single color gluon exchange in an asymptotically free theory. Since the interaction of light confined quarks depends on only one length scale, while that of heavy confined quarks depends on two length scales, it is argued that the spin-dependent interactions are qualitatively different in the cases. Phenomenological evidence suggests that the spin-dependent interactions of light quarks are short-ranged only, while that of heavy quarks are predominantly long-ranged. It is proposed that a measurement of the F∗-F mass-difference will help clarify the nature of a possible long-ranged spin-spin interaction of strange quarks.

A path integral construction of superconformal field theories is presented based on gauged supersymmetric Wess-Zumino-Witten actions. The conformal charge of the model is identical to that of a GKO construction. Ghost modes appear in the formalism as a result of gauge fixing. As a consequence, the holomorphic stress-tensor T ( z ) and superconformal generator G ( z ) obtained in the construction have ghost contributions. Weak operator first-class constraints restrict the theory to physical states which satisfy the constraints. The superconformal algebra closes when evaluated between ghost-free physical states.

A simple relativistic potential model is constructed in order to describe meson spectroscopy in a unified way, encompassing both light- and heavy-quark systems. A linear potential, transforming as the fourth component of a vector potential, is assumed in accordance with quark-confinement mechanisms appropriate to gauge theories. Scaling arguments are used to derive the Regge behavior of the model. We present evidence that the forces which confine quarks are essentially independent of quark species. The over-all systematics of our predictions for meson energy levels and leptonic decay widths give support to the usefulness of the model. We comment on the application of asymptotic freedom as a means of estimating decay rates which violate the Okubo - Zweig - Iizuka rule.

The systematics of L = 2 light meson spin dependent spectra is examined within the context of the spectroscopy of other meson states. A relatively model independent measure of the average quark velocity in light meson spectroscopy is presented. A qualitative picture of (q q ) valence quark spectra with relativistic kinematics seems to emerge from the data.

Recent results from quantum chromodynamics (QCD) are shown to be consistent with the generalized Breit-type phenomenological Hamiltonian previously proposed for the spin-dependent spectroscopy of quark-antiquark states. In particular, the concept of a short-distance and long-distance quark-gluon chromomagnetic moment, with different qualitative behavior for light and heavy quarks, is compatible with QCD. An induced axial-vector exchange, previously suggested by Feinberg and Sucher, also seems to be implied by the field-theoretic calculations.

Vacuum polarization at long distances for confined heavy-quark-antiquark (QQ-bar) pairs is considered. The vacuum-polarization-corrected static potential is shown to have a radial dependence which should allow interpolation between charmonium, upsilon states, and other heavy QQ-bar systems. It is argued that the static, confining potential cannot grow faster than a linear potential at large distances, within the framework of this analysis.

An arbitrary, renormalizable non-Abelian gauge theory with gauge group $\mathfrak{g}$, and arbitrary scalar and fermion representation structure is considered. It is shown that all the gauge vector mesons of the theory lie on a Regge trajectory if and only if $\mathfrak{g}$ is semisimple, i.e., Abelian subgroups are excluded. Implications for unified and grand unified theories of the weak and electromagnetic interactions are discussed. The photon, which does not Reggeize in the Weinberg-Salam theory, will lie on a Regge trajectory in a grand unified theory. If the Higgs-meson mass of the electroweak theory is large (\ensuremath{\gtrsim} 300 GeV, say), then Regge recurrences of the intermediate vector bosons should occur at energies of the order of 2-4 TeV. If the Higgs boson of the unified theory is light ( 100 GeV), then Regge recurrences of the gauge mesons are not expected for energies below the grand-unification mass of order ${{\ensuremath{\mu}}_{W}}^{2}$ $\mathrm{exp}(\frac{1}{{g}^{2}})$.

It is shown that the anomalous divergence of the supercurrent in a supersymmetric non-Abelian gauge theory may be removed at the one-loop level by coupling three scalar multiplets in the adjoint representation to the supersymmetric Yang-Mills multiplet.

It is demonstrated that an anomaly exists for the supercurrent in a supersymmetric non-Abelian gauge theory. Since no gauge particle is coupled to the current, the anomaly does not alter the renormalizability of the theory. Some consequences of the anomaly are discussed.

It is shown how to construct effective lagrangians to the two-loop level for non-abelian gauge theories, quantized in background field gauge. This construction is no more difficult than the analogous computation in abelian gauge theories when minimal subtraction is employed. It is argued that for three or more loops, one can no longer separate heavy or mixed light-heavy graphs in an intermediate renormalization, and the more general algorithm presented by us in an earlier work must be employed even in background field gauge.

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin 3 2 quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.

We show explicitly, to the two-loop level, that the decoupling theorem of Appelquist and Carazzone is valid, and a consistent light effective field theory exists, for quantum electrodynamics in arbitrary α-gauges, and non-abelian gauge theory in α = 0, Landau gauge, renormalized by minimal subtraction.

Vacuum polarization at long distances for confined heavy-quark--antiquark (QQ-bar) pairs is considered. It is argued that the static confining potential cannot grow faster than a linear potential at large distances. The vacuum-polarization-corrected potential is a flavor-independent potential which allows interpolation between charmonium, UPSILON and other QQ-bar systems.

Evidence from meson spectroscopy is presented to support the view that the effective interaction between quark-antiquark pairs is a long-range scalar confining force, together with a short-range Coulomb-type vector exchange governed by the underlying quantum chromodynamics. As a result, it is prediced that the $^{3}P$-wave charmed mesons and mesons of the type ($b\overline{u}$) and ($b\overline{s}$) will be inverted multiplets. Discovery of such an effect would provide strong evidence for an effective scalar confining force. It is argued, on the basis of the systematics of the tensor force in the ordinary mesons, that there are important induced tensor forces in the $I=1$ and $I=\frac{1}{2}$ $P$-wave meson multiplets. A qualitative discussion suggests that the induced tensor forces are due to couplings of the $J=1$, $I=1$ and $I=\frac{1}{2}$ mesons to open decay channels. As a result, the ${A}_{1}$, $B$, ${Q}_{A}$, and ${Q}_{B}$ mesons appear to have substantial mixings with $(q\overline{q})(q\overline{q})$ configurations.

An arbitrary, renormalizable non-Abelian gauge theory with gauge group $\mathcal{G}$ and arbitrary scalar and fermion structure is considered. Necessary conditions for all the fermions of the theory to lie on Regge trajectories are derived. If no fermion transforms as a singlet under $\mathcal{G}$, then all fermions Reggeize. If some fermions transform as singlets under $\mathcal{G}$, then certain group-theoretic constraints on the fermion mass matrix must be satisfied if all fermions are to Reggeize. These methods are applied to the Weinberg-Salam and grand unified theories. As a by-product of this study, kinematical-singularity-free, signatured helicity amplitudes are constructed which allow for $P$ and $\mathrm{CP}$ violation. Such amplitudes may be useful for applications outside the context of the Regge program.

The supercurrent anomalies of the supercurrent S μ of the supersymmetric Yang-Mills theory in Wess-Zumino gauge are computed using the supersymmetric dimensional regulator of Siegel. It is shown that γ μ S μ =0 and ∂ μ S μ ≠0 in agreement with an earlier calculation based on the Adler-Rosenberg method. The problem of exhibiting the chiral anomaly and a regulator for local supersymmetry suggests that the interpretation of dimensional reduction in component language is incomplete.

The large S-state hyperfine splittings and the spacing of the P-states of charmonium can be explained qualitatively by an effective quark-gluon anomalous magnetic moment of 1 quark magneton within the context of a nonrelativistic linear potential model.

A path integral formulation of G/H conformal theories is presented, based on gauged Wess-Zumino-Witten actions. The conformal charge of the model is c=cG−cH, exactly as in the GKO construction. Ghost modes appear in the formalism as a result of gauge fixing. As a consequence, the holomorphic stress-tensor T(z) obtained in our construction has ghost contributions. We find T(z)=TG−TH only for matrix elements of physical states which are also ghost free.

We discuss the canonical quantization of the pion-skyrmion system. The presence of derivative couplings and mixing between the pion degrees and collective coordinates requires that care be exercized in the quantization in order to preserve chirality and soft-pion theorems. As an application of these methods we calculate the leading soft-pion radiative corrections to the skyrmion mass and pion emission from skyrmions.

Bosonic and fermionic partition functions on the two-dimensional torus are explicitly calculated to establish a Bose-Fermi equivalence for each fundamental representation of every simple-laced group G. A one-to-one correspondence exists for bosons with momenta generated by the root lattice of G shifted by the element w k , where w k is a minimal weight of G, i.e. and element of the center of the covering group of G, and fermions with generalized boundary conditions ψ → (exp iθk)ψ (under rotation around the torus) where exp(iθk) is the same element of Z as is w k . The non-orthogonal weight lattices of G are converted into orthogonal lattices with constraints. It is shown that only for spin(2N) can these constraints be written as projection operators, which correspond to sums over spin structure in fermion language. For SU(N), E6 and E7 the appropriate constraints are imposed by coupling the fermions to background U(1) world-sheet gauge fields which act as Lagrange multipliers, i.e. the equivalence is to constrained fermions. Explicit modular invariant partition functions are presented for closed strings compactified ti simply-laced groups associated to Kac-Moody algebras with central charge k = 1.

It is shown by direct computation that the supersymmetry Ward identity for the supersymmetric Yang-Mills theory can be satisfied at the one-loop level in the Wess-Zumino gauge when one uses dimensional regularization with the prescription ${\ensuremath{\gamma}}^{\ensuremath{\mu}}{\ensuremath{\gamma}}_{\ensuremath{\mu}}=4$, and performs the Dirac algebra in four dimensions. The result is found to be valid for arbitrary covariant gauge-fixing functionals. A particular gauge, $\ensuremath{\xi}=\ensuremath{-}3$, is found for which the supersymmetry transformations of both renormalized and unrenormalized fields are finite and well defined. In this same gauge, one-loop renormalization constants for two-, three-, and four-point one-particle-irreducible Green's functions are found to be equal.

Two-dimensional non-abelian Bose-Fermi equivalence in the presence of two-dimensional background gauge and gravitational fields is discussed for the k>1 WZW model and fermions constrained through coupling to gauge fields which act as Lagrange parameters. The equivalence is shown to be valid only when the gravitational field can be decoupled, which occurs when the central charge coincides with that obtained from current algebra.

The question of the Reggeization of the elementary particles in renormalizable gauge theories with the Higgs-Kibble mechanism is examined. It is concluded that the massive non-Abelian gauge vector mesons and $J=\frac{1}{2}$ fermions of these theoreis lie on Regge trajectories in every case in which a counting criterion due to Mandelstam is satisfied. Several explicit examples are presented which verify that the necessary factorization condition of the Born helicity matrices is satisfied at $J=1$ and $J=\frac{1}{2}$, supporting this conclusion.