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Howard J. Schnitzer

Publications and source records attributed to Howard J. Schnitzer.

At least 55 records · Page 3Linked to original sources
arXiv2008

Two-loop graviton scattering relation and IR behavior in N=8 supergravity

We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N=8 supergravity. Specifically we show that the infrared divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms.

hep-th↗
arXiv2007

Confinement/Deconfinement Transition of Large N Gauge Theories in Perturbation Theory with N_f Fundamentals: N_f/N Finite

In hep-th/0402219 we considered 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}x time, with N_f/N finite. This class of theories undergo a 3rd order deconfinement transition. As a consequence it was proposed that the dual string theory has a 3rd order phase-transition to a black hole at high temperature. In this paper we argue that the same conclusions are valid for such theories at any finite order in perturbation theory in the 't Hooft coupling lambda and N_f/N. It is conjectured that this continues to hold at strong coupling and finite value of N_f/N < (1/lambda), which suggests that the supergravity approximation to the dual string theory has a 3rd order thermal phase transition to a large black hole.

hep-th↗
arXiv2007

Regge behavior of gluon scattering amplitudes in N=4 SYM theory

It is shown that the four-gluon scattering amplitude for N=4 supersymmetric Yang-Mills theory in the planar limit can be written, in both the weak- and strong-coupling limits, as a reggeized amplitude, with a parent trajectory and an infinite number of daughter trajectories. This result relies crucially on the fact that the leading IR-divergence and the finite log^2(s/t)-dependent piece of the amplitude are characterized by the same function for all values of the coupling, as conjectured by Bern, Dixon, and Smirnov, and proved by Alday and Maldacena in the strong-coupling limit. We use the Alday-Maldacena result to determine the strong-coupling Regge trajectory.

hep-th↗
arXiv2007

Reggeization of N=8 Supergravity and N=4 Yang-Mills Theory II

The loop expansion for the n-point functions of N=4 Yang-Mills theory and N=8 supergravity can be formulated as the loop expansion of scalar field theory with an infinite subclass being the ladder diagrams. We consider the sum of ladder diagrams for gluon-gluon and graviton-graviton scattering in the Regge limit. The reggeization of the gluon and the graviton is discussed in this context and that of hep-th/0701217. If the Bern, Dixon, Smirnov conjecture for planar gluon-gluon scattering is correct, then the ladder sum for SU(N) gauge theory at large N, correctly gives the Regge limit, with Regge trajectory function proportional to the cusp anomalous dimension. In graviton-graviton scattering it is argued that the graviton lies on a Regge trajectory. Regge cuts are also present due to infinite sums of non-planar graphs. The multiple exchange of Regge poles in non-planar graphs can give a countable infinite number of moving Regge cuts which accumulate near s=0. It is conjectured that this may be related to the infinite number of non-perturbative massless states which remain in the limit discussed by Green, Ooguri and Schwarz.

hep-th↗
arXiv2007

Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory

We study the WZW, Chern-Simons, and 2d qYM theories with gauge group U(N). The U(N) WZW model is only well-defined for odd level K, and this model is shown to exhibit level-rank duality in a much simpler form than that for SU(N). The U(N) Chern-Simons theory on Seifert manifolds exhibits a similar duality, distinct from the level-rank duality of SU(N) Chern-Simons theory on S^3. When q = e^{2 pi i/(N+K)}, the observables of the 2d U(N) qYM theory can be expressed as a sum over a finite subset of U(N) representations. When N and K are odd, the qYM theory exhibits N <--> K duality, provided q = e^{2 pi i/(N+K)} and theta = 0 mod 2 pi /(N+K).

hep-th↗
arXiv2007

Reggeization of N=8 Supergravity and N=4 Yang--Mills Theory

We show that the gluon of N=4 Yang--Mills theory lies on a Regge trajectory, which then implies that the graviton of N=8 supergravity also lies on a Regge trajectory. This is consistent with the conjecture that N=8 supergravity is ultraviolet finite in perturbation theory.

hep-th↗
arXiv2006

Twisted D-branes of the SU(N)_K WZW model and level-rank duality

We analyze the level-rank duality of omega_c-twisted D-branes of SU(N)_K (when N and K>2). When N or K is even, the duality map involves Z_2-cominimal equivalence classes of twisted D-branes. We prove the duality of the spectrum of an open string stretched between omega_c-twisted D-branes, and ascertain the relation between the charges of level-rank-dual omega_c-twisted D-branes.

hep-th↗
arXiv2006

Level-rank duality of untwisted and twisted D-branes

Level-rank duality of untwisted and twisted D-branes of WZW models is explored. We derive the relation between D0-brane charges of level-rank dual untwisted D-branes of su(N)_K and sp(n)_k, and of level-rank dual twisted D-branes of su(2n+1)_2k+1. The analysis of level-rank duality of twisted D-branes of su(2n+1)_2k+1 is facilitated by their close relation to untwisted D-branes of sp(n)_k. We also demonstrate level-rank duality of the spectrum of an open string stretched between untwisted or twisted D-branes in each of these cases.

hep-th↗
arXiv2006

Level-rank duality of D-branes on the SU(N) group manifold

The consequences of level-rank duality for untwisted D-branes on an SU(N) group manifold are explored. Relations are found between the charges of D-branes (which are classified by twisted K-theory) belonging to su(N)_K and su(K)_N WZW theories, in the case of odd N+K. An isomorphism between the charge algebras is also demonstrated in this case.

hep-th↗
arXiv2005

Multipole Radiation in Lorentz Gauge

The multipole expansion for electromagnetic radiation, valid for all wave-lengths and all distances from bounded sources, is presented in Lorentz gauge, rather than the usual Coulomb gauge. This gauge is likely to be preferred in applications where one wishes to maintain manifest Lorentz invariance. The presentation also serves as a useful exercise in the use of vector spherical harmonics.

physics.class-ph↗
arXiv2005

More Pendants for Polya: Two loops in the SU(2) sector

We extend the methods of Spradlin and Volovich to compute the partition function for a conformally-invariant gauge theory on R x S^3 in which the dilatation operator is represented by a spin-chain Hamiltonian acting on pairs of states, not necessarily nearest neighbors. A specific application of this is the two-loop dilatation operator of the planar SU(2) subsector of the N=4 SU(N) super Yang-Mills theory in the large-N limit. We compute the partition function and Hagedorn temperature for this sector to second order in the gauge coupling. The Hagedorn temperature is to be interpreted as giving the exponentially-rising portion of the density of states of the SU(2) sector, which may be a signal of stringy behavior in the dual theory.

hep-th↗
arXiv2004

Many roads lead to N=2 Seiberg-Witten theory

The Seiberg-Witten solution plays a central role in the study of N=2 supersymmetric gauge theories. As such, it provides a proving ground for a wide variety of techniques to treat such problems. In this review we concentrate on the role of IIA string theory/M theory and the Dijkgraaf-Vafa matrix model, though integrable models and microscopic instanton calculations are also of considerable importance in this subject.

hep-th↗
arXiv2004

Confinement/Deconfinement Transition of Large N Gauge Theories with N_f Fundamentals: N_f/N Finite

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} x 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 {\cal O} (N^2_f), 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.

hep-th↗
arXiv2003

Gauged Vector Models and Higher-Spin Representations in AdS_5

Motivated by the work of Klebanov and Polyakov [hep-th/0210114] on the relationship of the large N O(N) vector model in three-dimensions to AdS_4 and higher spin representations, we attempt to find analogous connections for AdS_5. Since the usual O(N) vector model in four-dimensions is inconsistent, we consider the (consistent) large N gauged vector model and a N=1 supersymmetric analogue in four-dimensions. Both these theories have UV and IR fixed points, and are candidates for a (α')^-1 expansion in AdS_5, a conjectured AdS_5/CFT correspondence and higher-spin representations in the bulk theory.

hep-th↗
arXiv2003

One-instanton predictions for non-hyperelliptic curves derived from M-theory

One-instanton predictions are obtained from certain non-hyperelliptic Seiberg-Witten curves derived from M-theory for N=2 supersymmetric gauge theories. We consider SU(N_1) x SU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with hypermultiplets in the defining representations of SU(N_1) and SU(N_2). We also consider SU(N) gauge theory with a hypermultiplet in the symmetric or antisymmetric representation, together with hypermultiplets in the defining representation. The systematic perturbation expansion about a hyperelliptic curve together with the judicious use of an involution map for the curve of the product groups provide the principal tools of the calculations.

hep-th↗
arXiv2002

An orientifold of adS_5xT^11 with D7-branes, the associated alpha'^2- corrections and their role in the dual N=1 Sp(2N+2M)xSp(2N) gauge theory

We study the N=1 Sp(2N+2M)xSp(2N) gauge theory on a stack of N physical and M fractional D3-branes in the background of an orientifolded conifold. The gravity dual is a type IIB orientifold of adS_5xT^11 (with certain background fluxes turned on) containing an O7-plane and 8 D7-branes. In the conformal case (M=0), we argue that the alpha'^2-corrections localized on the 8 D7-branes and the O7-plane should give vanishing contributions to the supergravity equations of motion for the bulk fields. In the cascading case (M not equal to 0), we argue that the alpha'^2-terms give rise to corrections which in the dual Sp(2N+2M)xSp(2N) gauge theory can be interpreted as corrections to the anomalous dimensions of the matter fields.

hep-th↗
arXiv2002

pp-wave limits and orientifolds

We study the pp-wave limits of various elliptic models with orientifold planes and D7-branes, as well as the pp-wave limit of an orientifold of adS_5 x T^{11}. Many of the limits contain both open and closed strings. We also present pp-wave limits of theories which give rise to a compact null direction and contain open strings. Maps between the string theory states and gauge theory operators are proposed.

hep-th↗