arXiv subjects

Nelia Mann

Publications and source records attributed to Nelia Mann.

16 recordsLinked to original sources

arXiv2022

Glueball-Meson Mixing In Holographic QCD

Top-down holographic QCD models often work in the "probe" (or "quenched") limit, which assumes that the number of colors is much greater than the number of flavors. Relaxing this limit is essential to a fuller understanding of holography and more accurate phenomenological predictions. In this work, we focus on a mixing of glueball and meson mass eigenstates that arises from the DBI action as a finite Nf/Nc effect. For concreteness, we work in the Witten-Sakai-Sugimoto model, and show that this mixing must be treated in conjunction with the backreaction of the flavor branes onto the background geometry. Including the backreaction with the simplification that it is "smeared out" over the compact transverse direction, we derive a corrected effective action for the vector glueball and scalar states. Along the way, we observe a Stueckelberg-like mechanism that restores translation invariance in the transverse direction. We also derive a general technique, that lends itself easily to numerics, for finding mass eigenstates of Lagrangians with vector-scalar mixing. We then calculate the first order corrections to the mass spectra of both the vector and scalar particles, and show that the term that explicitly mixes vector and scalar states is the most significant correction to the masses of low-lying scalar mesons.

hep-th↗

arXiv2020

Old Quantization, Angular Momentum, and Nonanalytic Problems

We explore the method of old quantization as applied to states with nonzero angular momentum, and show that it leads to qualitatively and quantitatively useful information about systems with spherically symmetric potentials. We begin by reviewing the traditional application of this model to hydrogen, and discuss the way Einstein-Brillouin-Keller quantization resolves a mismatch between old quantization states and true quantum mechanical states. We then analyze systems with logarithmic and Yukawa potentials, and compare the results of old quantization to those from solving Schrodinger's equation. We show that the old quantization techniques provide insight into the spread of energy levels associated with a given principal quantum number, as well as giving quantitatively accurate approximations for the energies. Analyzing systems in this manner involves an educationally valuable synthesis of multiple numerical methods, as well as providing deeper insight into the connections between classical and quantum mechanical physics.

quant-ph↗

arXiv2019

Chain Formation in a 2-Dimensional System of Hard Spheres with a Short Range, Anisotropic Interaction

We analyze a generalization of the hard sphere dipole system in two dimensions in which the interaction range of the interaction can be varied. We focus on the system in the limit the interaction becomes increasingly short-ranged, while the temperature becomes low. By using a cluster expansion and taking advantage of low temperatures to perform saddle-point approximations, we argue that a well defined double limit exists in which the only structures which contribute to the free energy are chains. We then argue that the dominance of chain structures is equivalent to the dominance of chain diagrams in a cluster expansion, but only if the expansion is performed around a hard sphere system (rather than the standard ideal gas). We show that this leads to non-standard factorization rules for diagrams, and use this to construct a closed-form expression for the free energy at low densities. We then compare this construction to several models previously developed for the hard sphere dipole system in the regime where chain structures dominate, and argue that the comparison provides evidence in favor of one model over the others. We also use this construction to incorporate some finite density effects though the hard sphere radial distribution function, and analyze the impact of these effects on chain length and the equation of state.

cond-mat.stat-mech↗

arXiv2017

A Second Look at String-Inspired Models for Proton-Proton Scattering via Pomeron Exchange

We re-examine a string dual model for elastic proton-proton scattering via Pomeron exchange. We argue that the method of "Reggeizing" a propagator to take into account an entire trajectory of exchanged particles can be generalized, in particular by modifying the value of the mass-shell parameter in the model. We then fit the generalized model to scattering data at large s and small t. The fitting results are inconclusive, but suggest that a better fit might be obtained by allowing the mass-shell to vary. The model fits the data equally well (roughly) for a wide range of values of the mass-shell parameter, but the other fitting parameters (the slope and intercept of the Regge trajectory, and the coupling constant and dipole mass from the proton-proton-glueball coupling) are then inconsistent with what we expect. On the other hand, using the traditional method of Reggeization generates a weaker fit, but the other parameters obtain more physically reasonable values. In analyzing the fitting results, we also found that our model is more consistent with the sqrt(s) = 1800 GeV coming from the E710 experiment than that coming from the CDF experiment, and that our model has the greatest discrepancy with the data in the range 0.5 GeV^2 < |t| < 0.6 GeV^2, suggesting that the transition from soft Pomeron to hard Pomeron may occur closer to t = -0.5 GeV^2 rather than t = -0.6 GeV^2 as previously thought.

hep-ph↗

arXiv2016

Central Production of $η$ via Double Pomeron Exchange and Double Reggeon Exchange in the Sakai-Sugimoto Model

We use holographic QCD to study Pomeron- and Reggeon-mediated central production in Regge regime hadronic scattering. We focus specifically on $η$ production in proton-proton collisions. While previous work studied the Pomeron-mediated process, the mesonic Regge trajectories ("Reggeons") we now incorporate contribute significantly at experimentally probed energies. We use the five-point open string amplitude (in flat space) to construct approximate propagators for the Reggeon states, and the five-point closed string amplitude for the Pomeron. Using these "holographic" Reggeons and Pomerons, and low-energy couplings derived in the Sakai-Sugimoto model, we compute the differential and total cross sections at $\sqrt{s}$ =29.1 GeV. Our calculation of the total cross section is $σ=236 \ \mathrm{nb}$, while the experimentally measured value is $σ= 3859 \ \mathrm{nb}$. The discrepancy between our result and the measured value may indicate that our model systematically underestimates the values of the relevant coupling constants.

hep-ph↗

arXiv2014

Central Production of Eta and Eta-prime via Double Pomeron Exchange in the Sakai-Sugimoto Model

We construct a string-inspired model for the central production of $η$ and $η'$ mesons in proton-proton collisions, via double Pomeron exchange. Using general symmetry considerations, we construct a low-energy differential cross section for double glueball exchange in terms of some undetermined coupling constants and form factors. We extend this model to the Regge regime, replacing the glueball propagators with Pomeron trajectories, and modifying the interaction term by a factor derived from the 5-string scattering amplitude in flat space. We then fix the couplings which remain undetermined, using the Sakai-Sugimoto framework to model low-energy QCD. Finally, we generate a simulation of the scattering process at $\sqrt{s} = 29.1 GeV$, where double Pomeron exchange should play a role (secondary to double Reggeon exchange). We focus on the dependence of the scattering cross section on the angle between the scattered protons in the transverse plane. The results exhibit a definite deviation from the angular dependence that arises as a consequence of natural parity violation alone. The amount of deviation is primarily determined by couplings that come from the Chern-Simons action of the AdS/QCD supergravity dual, which is directly related to the QCD gravitational anomaly, and thus constitutes a universal part of any five-dimensional string/gravity dual theory of QCD. We argue that this makes the high energy central production of pseudoscalar mesons an interesting probe of AdS/QCD models.

hep-ph↗

arXiv2010

The Pomeron contribution to p p and p bar p scattering in AdS/QCD

We consider the differential and total cross sections for proton-proton and proton-antiproton scattering in the Regge regime from the point of view of string dual models of QCD. We argue that the form factor which appears in the differential cross section is related to the matrix element of the stress tensor between proton states and give a procedure for computing the strength of the coupling of the Pomeron trajectory to the proton. We compute this coupling in the Sakai-Sugimoto model and find excellent agreement with the data at large $s$ and small $t$. The form factor can be estimated in the Skyrme model or in AdS/QCD models and gives a stiffer form factor than the commonly used electromagnetic form factor, in agreement with our fits to data. Our model is also in good agreement with the measured ratio of real to imaginary parts of the forward scattering amplitude at large $s$.

hep-ph↗

arXiv2010

Setting the scale of the p p and p bar p total cross sections using AdS/QCD

This paper is an addendum to our earlier paper \cite{pom} where we computed the Pomeron contribution to $p ~ p$ and $p ~ \bar p$ scattering in AdS/QCD. The model of \cite{pom} depends on four parameters: the slope and intercept of the Pomeron trajectory $α'_c, α_c(0)$, a mass scale $M_d$ which determines a form factor entering into matrix elements of the energy-momentum tensor, and a coupling $λ_{\cal P}$ between the lightest spin $2$ glueball and the proton which sets the overall scale of the total cross section. Here we perform a more detailed computation of $λ_{\cal P}$ in the Sakai-Sugimoto model using the construction of nucleons as instantons of the dual 5d gauge theory and an effective 5d fermion description of these nucleons which has been successfully used to compute a variety of nucleon-meson couplings. We find $λ_{\cal P,{\rm SS}} \simeq 6.38 ~ {\rm GeV}^{-1}$ which is in reasonable agreement with the value $λ_{{\cal P},{\rm fit}} = 8.28 ~ {\rm GeV}^{-1}$ determined by fitting single Pomeron exchange to data.

hep-th↗

arXiv2008

Wrapping Interactions and the Konishi Operator

We present a calculation of the four-loop anomalous dimension of the SU(2) sector Konishi operator in N=4 SYM, as an example of "wrapping" corrections to the known result for long operators. We use the known dilatation operator at four loops acting on long operator, and just calculate those diagrams which are affected by the change from operator length L > 4 to L = 4. We find that the answer involves a Zeta[5], so it has trancendentality degree five. Our result differs from previous proposals and calculations. We also discuss some ideas for extending this analysis to determine finite size corrections for operators of arbitrary length in the SU(2) sector.

hep-th↗

arXiv2006

Classical Open String Integrability

We present a simple procedure to construct non-local conserved charges for classical open strings on coset spaces. This is done by including suitable reflection matrices on the classical transfer matrix. The reflection matrices must obey certain conditions for the charges to be conserved and in involution. We then study bosonic open strings on $AdS_5\times S^5$. We consider boundary conditions corresponding to Giant Gravitons on $S^5$, $AdS_4\times S^2$ D5-branes and $AdS_5 \times S^3$ D7-branes. We find that we can construct the conserved charges for the full bosonic string on a Maximal Giant Graviton or a D7-brane. For the D5-brane, we find that this is possible only in a SU(2) sub-sector of the open string. Moreover, the charges can not be constructed at all for non-maximal Giant Gravitons. We discuss the interpretation of these results in terms of the dual gauge theory spin chains.

hep-th↗

arXiv2006

The SU(2) Long Range Bethe Ansatz and Continuous Integrable Systems

We explore the relationship between the SU(2) sector of a general integrable field theory and the all-loop guess for the anomalous dimensions of SU(2) operators in N=4 super Yang-Mills theory. We demonstrate that the SU(2) structure of a nested Bethe ansatz alone reproduces much of the all-loop guess without depending on the details of the particular field theory. We speculate on the implications of this for strings in AdS_5 X S^5 being described by the multi-particle states of an integrable worldsheet theory, and relate the techniques here to the known relationship between the Hubbard model and the all-loop guess.

hep-th↗

arXiv2005

Bethe Ansatz for a Quantum Supercoset Sigma Model

We study an integrable conformal OSp(2m + 2|2m) supercoset model as an analog to the AdS_5 X S^5 superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle density in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the well-studied classical limit, the lambda^{-1/2} effects and the 1/J effects. Our approach captures the first type, but not the second.

hep-th↗

arXiv2005

Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter

We demonstrate that the one-loop anomalous dimension matrix in N = 2 SYM with a single chiral hypermultiplet of fundamental matter, which is dual to AdS_5 X S^5 with a D7-brane filling AdS_5 and wrapped around an $^3 in the S^5, is an integrable open spin chain Hamiltonian. We also use the doubling trick to relate these open spin chains to closed spin chains in pure N = 4 SYM. By using the AdS/CFT correspondence, we find a relation between the corresponding open and closed strings that differs from a simple doubling trick by terms that vanish in the semiclassical limit. We also demonstrate that in some cases the closed string is simpler and easier to study than the corresponding open string, and we speculate on the nature of corrections due to the presence of D-branes that this implies.

hep-th↗

arXiv2004

Finite Density States in Integrable Conformal Field Theories

We study states of large charge density in integrable conformal coset models. For the O(2) coset, we consider two different S-matrices, one corresponding to a Thirring mass perturbation and the other to the continuation to O(2+epsilon). The former leads to simplification in the conformal limit; the latter gives a more complicated description of the O(2) system, with a large zero mode sector in addition to the right- and left-movers. We argue that for the conformal O(2+2M|2M) supergroup coset, the S-matrix is given by the analog of the O(2+epsilon) construction.

hep-th↗

arXiv2004

Integrable Open Spin Chains in Defect Conformal Field Theory

We demonstrate that the one-loop dilatation generator for the scalar sector of a certain perturbation of N=4 Super Yang-Mills with fundamentals is the Hamiltonian of an integrable spin chain with open boundary conditions. The theory is a supersymmetric defect conformal field theory (dCFT) with the fundamentals in hypermultiplets confined to a codimension one defect. We obtain a K-matrix satisfying a suitably generalized form of the boundary Yang-Baxter equation, study the Bethe ansatz equations and demonstrate how Dirichlet and Neumann boundary conditions arise in field theory, and match to existing results in the plane wave limit.

hep-th↗

arXiv2003

AdS Holography in the Penrose Limit

We study the holographic description of string theory in a plane wave spacetime by taking the Penrose limit of the usual AdS/CFT correspondence. We consider three-point functions with two BMN operators and one non-BMN operator; the latter should go over to a perturbation of the dual CFT. On the string side we take the Penrose limit of the metric perturbation produced by the non-BMN operator, and the BMN state propagates in this perturbed background. The work of Lee, Minwalla, Rangamani, and Seiberg shows that for chiral operators the AdS three-point functions agree with those calculated in the free gauge theory. However, when this is reduced to an effective plane wave amplitude by truncating the amplitude to propagate from the AdS boundary to the Penrose geodesic, we find a puzzling mismatch. We discuss possible resolutions, and future directions.

hep-th↗