Abstract We consider the gauge/gravity correspondence between maximally supersymmetric Yang–Mills theory in (p + 1) dimensions and superstring theory on the near-horizon limit of the Dp-brane solution. The string-frame metric is AdS$_{p + 2}$ × S$^{8 − p}$ times a Weyl factor, and there is no conformal symmetry except for p = 3. In a previous paper by one of the present authors, the free-field result of gauge theory has been reproduced from string theory for a particular operator that has angular momentum along S$^{8 − p}$. In this paper, we extend this result to operators that have angular momenta along AdS$_{p + 2}$. Our approach is based on a Euclidean formulation proposed by Dobashi et al. [Nucl. Phys. B 665, 94 (2003)] and on the “string bit” picture. We first show that the spinning string solution in Lorentzian AdS, found by Gubser et al. [Nucl. Phys. B 636, 99 (2002)], can be recast in a form that connects two points on the boundary of Euclidean AdS. The transition amplitudes of such strings can be interpreted as gauge theory correlators. We study the case of zero gauge coupling by ignoring interactions among string bits (massless particles in 10D spacetime that constitute a string), and show that the free-field results of gauge theory are reproduced.

Japan

Tomotaka Kitamura

Shoichiro Miyashita

Yasuhiro Sekino

Rotating particles in AdS: Holography at weak gauge coupling and without conformal symmetry

Abstract We investigate the relation between -matrix unitarity () and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from the -matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher-derivative kinetic term do not necessarily satisfy the unitarity bound because of the negative-norm states. In these theories it is not known whether the -matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper, by relaxing the assumption of norm positivity we derive a bound on scattering amplitudes weaker than the unitarity bound, which may be used as a consistency requirement for -matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints.

Yugo Abe

Takeo Inami

Keisuke Izumi

Toshifumi Noumi

-matrix Unitarity and Renormalizability in Higher-derivative Theories

We investigate the ultraviolet (UV) behavior of two-scalar elastic scattering with graviton exchanges in higher-curvature gravity theory. In Einstein gravity, matter scattering is shown not to satisfy the unitarity bound at tree level at high energy. Among some of the possible directions for the UV completion of Einstein gravity, such as string theory, modified gravity, and inclusion of high-mass/high-spin states, we take gravity coupled to matter. We show that matter scattering with graviton interactions satisfies the unitarity bound at high energy, even with negative norm states due to the higher-order derivatives of metric components. The difference in the unitarity property of these two gravity theories is probably connected to that in another UV property, namely, the renormalizability property of the two.

South Korea

Matter scattering in quadratic gravity and unitarity

We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability conditions are modified from those in relativistic theories. We show that for renormalizability, an extended version of the power-counting condition is required in addition to the conventional one. The unitarity bound for S-matrix elements also gives stronger constraints on interaction terms because of the reference frame dependence of scattering amplitudes. We prove that both unitarity and renormalizability require identical conditions as in the case of conventional relativistic theories.

Toshiaki Fujimori

Taiwan

Spain

Tree-level unitarity and renormalizability in Lifshitz scalar theory