https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=1956&context=aspubs

Light-front holographic QCD and emerging confinement

Extreme and very-near-extreme spin $J$ Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges ${c}_{L}={c}_{R}=12J$. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic nonextreme values of the mass $M\ensuremath{\ne}\sqrt{J}$. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The $2\ensuremath{\pi}$ periodic identification of the azimuthal angle $\ensuremath{\phi}$ is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures ${T}_{L}={M}^{2}/2\ensuremath{\pi}J$ and ${T}_{R}=\sqrt{{M}^{4}\ensuremath{-}{J}^{2}}/2\ensuremath{\pi}J$. The well-known low-frequency scalar-Kerr scattering amplitudes coincide with correlators of a 2D CFT at these temperatures. Moreover, the CFT microstate degeneracy inferred from the Cardy formula agrees exactly with the Bekenstein-Hawking area law for all $M$ and $J$. These observations provide evidence for the conjecture that the Kerr black hole is dual to a ${c}_{L}={c}_{R}=12J$ 2D CFT at temperatures (${T}_{L},{T}_{R}$) for every value of $M$ and $J$.

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Hidden Conformal Symmetry of the Kerr Black Hole

In this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here gives a precise interpretation of holographic variables and quantities in AdS in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound states in physical space-time. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large $q^2$ the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low $q^2$ the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.

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Light-Front Holographic QCD and Emerging Confinement

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.

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The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities

The MEG experiment, designed to search for the $${\mu ^+ \rightarrow \hbox {e}^+ \gamma }$$
 decay, completed data-taking in 2013 reaching a sensitivity level of $${5.3\times 10^{-13}}$$
 for the branching ratio. In order to increase the sensitivity reach of the experiment by an order of magnitude to the level of $$6\times 10^{-14}$$
 , a total upgrade, involving substantial changes to the experiment, has been undertaken, known as MEG II. We present both the motivation for the upgrade and a detailed overview of the design of the experiment and of the expected detector performance.

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The design of the MEG II experiment

We construct a crossing symmetric basis for conformal four-point functions in momentum space by requiring consistent factorization. Just as scattering amplitudes factorize when the intermediate particle is on-shell, non-analytic parts of conformal correlators enjoy a similar factorization in momentum space. Based on this property, Polyakov, in his pioneering 1974 work, introduced a basis for conformal correlators which manifestly satisfies the crossing symmetry. He then initiated the bootstrap program by requiring its consistency with the operator product expansion. This approach is complementary to the ordinary bootstrap program, which is based on the conformal block and requires the crossing symmetry as a consistency condition of the theory. Even though Polyakov’s original bootstrap approach has been revisited recently, the crossing symmetric basis has not been constructed explicitly in momentum space. In this paper we complete the construction of the crossing symmetric basis for scalar four-point functions with an intermediate operator with a general spin, by using new analytic expressions for three-point functions involving one tensor. Our new basis manifests the analytic properties of conformal correlators. Also the connected and disconnected correlators are manifestly separated, so that it will be useful for the study of large N CFTs in particular.

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Momentum space approach to crossing symmetric CFT correlators

We apply a recently proposed Kerr/CFT correspondence to extremal supersymmetric five-dimensional charged spinning black holes, constructed by Breckenridge, Myers, Peet and Vafa. By computing the central charge of the dual CFT and Frolov–Thorne temperature, Cardy's formula succeeds in reproducing Bekenstein–Hawking area law.

Kerr/cft correspondence and five-dimensional bmpv black holes

We propose a supersymmetrisation of the cosmological constant in ordinary $$N=1$$
 supergravity that breaks supersymmetry spontaneously by a constant Fayet-Iliopoulos (FI) term associated to a U(1) symmetry. This term is a variation of a new gauge invariant FI term proposed recently, which is invariant under Kahler transformations and can be written even for a gauged R-symmetry on top of the standard FI contribution. The two terms are the same in the absence of matter but differ in its presence. The proposed term is reduced to a constant FI-term up to fermion interactions that disappear in the unitary gauge in the absence of any F-term supersymmetry breaking. The constant FI term leads to a positive cosmological constant, uplifting the vacuum energy from the usual anti-de Sitter supergravity to any higher value.

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The cosmological constant in supergravity

Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this construction to general dimensional conformal field theory. To facilitate the treatment of symmetric traceless tensors, we exploit techniques of spherical harmonics in general dimensions.

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Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension

We study the relation between exactly marginal deformations in a large class of N = 1 superconformal quiver gauge theories described by brane tilings and the degrees of freedom in the corresponding 5-brane systems. We show, with the help of NSVZ exact β functions, that there are generically d− 1 complex exactly marginal deformations of a gauge theory, where d is the perimeter of the corresponding toric diagram. We identify d− 3 complex marginal deformations as deformations of the brane system and the Wilson lines on it, and the other two, the diagonal gauge coupling and a β-like deformation, as background supergravity fields.

Hiroshi Isono

Papers

Momentum space approach to crossing symmetric CFT correlators

Kerr/cft correspondence and five-dimensional bmpv black holes

The cosmological constant in supergravity

Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension

Exactly Marginal Deformations of Quiver Gauge Theories as Seen from Brane Tilings