Chung-I Tan
Professor:
Physics
Phone: +1 401 863 2644
Phone 2: +1 401 863 1473
Chung-I_Tan@Brown.EDU
Professor Tan does research in theoretical particle physics, including: gauge/string duality; dynamics of hadrons; quantum chromodynamics; lattice gauge theories; large N expansion for QCD; matrix models and string theories; high-energy multiparticle phenomena; and statistical mechanics of strings at high-energy densities.
Biography
Professor Tan is a graduate of the University of California, Berkeley, where he also received the Ph.D. in Physics. Before joining the Brown faculty in 1970, he was an instructor at Princeton University. He has carried out research at the Brookhaven National laboratory, Lawrence Berkeley Laboratory, the Aspen Center for Physics, and CERN. He also served as Professor Associate at the University of Paris and University of Provence during his various sabbatical leaves. Professor Tan was Executive Officer of the Physics Department from 1992-1998. He began serving as the Chair of the Physics Department in 2004.
Research Description
Professor Chung-I Tan's research has focused on non-perturbative consequences of Quantum Chromodynamics (QCD). It has been a long held belief that QCD in a non-perturbative setting can be described by a string theory. The discovery by Maldacena of exact String/Gauge duality through the AdS/CFT mechanism now allows explicit calculation in some QCD like SUSY theories. The challenge is to abstract from these models fundamental concepts applicable to QCD. Prof. Tan has had a long interest in the formulation of the QCD string and in its phenomenological consequence. Specific efforts include the following areas: QCD from gauge/gravity duality, QCD at High Energy, Diffractive Scattering, Chirally improved lattice QCD, Confinement/de-confinement transitions, etc. What follows is a brief description of some of his research results during the past three years, with key references listed as footnotes. Some of these results have also been reported in various topical conferences and workshops.
These efforts have involved many active collaborators: Prof. R. Brower (Boston U.), Prof. E. M. Levin (Tel Aviv U.), Prof. S. Mathur (Ohio State U.), Prof. J. Polchinski, (UC, Santa Barbara), Prof. M. Strassler (U. of Washington), and Prof. C. Thorn (U. of Florida). Most recently, he has also begun a collaborative research program with Drs. D. Kharzeev and F. Karsch, (both of BNL), addressing certain issues in de-confinement transition where detectable signals can show up at RHIC and/or LHC.
QCD at High Energy and String/Gauge Duality: Prof. Tan with R. Brower, M. Strassler and J. Polchinski are now working on a range of problems investigating high-energy processes. In the absence of a complete formulation of a QCD string, the goal is to determine model independent consequence of String/Gauge duality for QCD. This general approach originates with the observation of Polchinski and Strassler that the wide-angle scattering of glueballs in a cut-off AdS5 background gave power behavior consistent with parton counting rules. This was extended to MQCD by Brower and Tan, where they noted also the subtlety of the Regge limit, and identified both the soft Pomeron trejectory for the tensor glueball and a hard component.
This program initiated by Brower, Polchinski, Strassler and Tan holds the promise of a new era where string/gauge duality can be used directly to provide insights on experimental observables at high energies. There are currently two seemingly conflicting interpretations of high energy amplitudes in QCD: One is the so-called Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron or hard' Pomeron, based on leading g2N log s perturbative approximation and the other is the soft Pomeron or a Regge pole that interpolates leading even-spin glueball resonances. Based on general arguments of conformal invariance, Brower, Polchinski, Strassler and Tan have shown that the strong coupling BFKL Pomeron emerges as a diffusion kernel (at t=0),
K(s,r,r') = s(?– 1)/ exp[-(ln r' - ln r)2/(4 D lns)],
which is identical to the BFKL weak coupling result with the replacements: diffusion in the virtuality kperp for the gluons replacing by diffusion in the 5th co-ordinate, r, and parameters, ? = 1 + ln 2 ?/?2 ? 2-2/ and D = 7 ?(3) ?/?2 ? ?/ respectively, where ? = g2YM Nc. Furthermore, in strong coupling it is easy to see how soft and hard components are mixed and how the hard component that dominates for t0. They have shown that the kernel, in a j-plane representation, satisfies a generalized diffusion equation in AdS5,
( j -2 + (1/2)[- ( 1/ ) (?u2 - 4) - ?'qcd t e- 2 u]) K(j,t; u, u') =? (u-u')
where u=log r. The AdS/CFT duality thus provides a natural synthesis of both features of soft and hard collision at high energies. There are many extensions of this research in the coming year, including the "odderon" exchange, doubly deep inelastic scattering and multiple Pomeron vertex algebra in AdS string theories. One crucial question is to see if, as conjectured in QCD, the so-called Onium-Onium scattering exposes simpler short distance features due to having both highly virtual targets and probes. Most importantly, this can also lead to a more systematic treatment of "diffractive Higgs production" and "pomeron structure function" at LHC energies. Marko Djuric, a PhD student working with Prof. Tan, is currently examining certain extension of the current work. Much more will be reported in the near future. Reactions from the community on their work have been swift, with many invitations for talks. In particularly, Prof. Tan has been invited to provide a detailed exposition of this work at "Strings & QCD", DESY, 5/16-20/2006.
Glueball and Stretched String Spectra: It is possible to test the viability of a dual QCD model by studying its spectral properties in comparison with lattice data. In the strong coupling limit (where the dual is super gravity in AdS-like background), Brower, Mathur and Tan have performed the first complete calculation of the low-lying glueball spectrum. The construction is based on Witten's suggestion to introduce into the AdS7xS4 background a Euclidean black hole breaking conformal and super symmetries leading to a confining theory with a QCD like spectrum. In spite of obvious limitation, the comparison with lattice data of Morningstar and Peardon is encouraging. The full bosonic multiplet for the IIA supergraviton is required to match the spectra. They next focused their attention on the spectral modes of the QCD string suspended between static quark sources at a fixed distance R, which offers an even more challenging problem with copious lattice data by Juge, Kuti and Morningstar. A semi-classical quantization has been carried out for a 5-d string in a general confining warped metric, which is asymptotic to AdS5 at the boundary and confining in the IR. The classical ground state energy fits extremely well the lattice determination of the static potential from the Coulombic to the linear confining regimes. In the semiclassical expansion, they find that the quantum excitations obey a set of simple wave equations,
[-?t2 + v2(x) ?x2] Xperp(t,x) = 0 and [-?t2 + v2(x) ?x2] ? (t,x) = M2(x) ?(t,x),
for two transverse and one radial (or longitudinal) modes respectively. The local velocity on the string v(x) equals to the speed of light in the middle but slowing down as they approach the quark endpoints. The new radial mode (not yet see in the lattice data) has a mass term proportional to the glueball mass. Qualitatively the energies agree with the data at intermediate R. To be able to follow string modes deep into the UV at small R is a tremendous challenge. At small separation one should approach the ``gluelump" spectrum of Bali and Pineda . These modes have yet to be computed using AdS/CFT but they should be present in the strong coupling limit. Prof. Tan has been invited to provide a review talk on "QCD Spectrum from AdS/CFT" and related topics at the IVth International Conf. on Quarks and Nuclear Physics, Madrid, 6/5-10, 2006.
Phenomenology of High Energy Diffractive Scattering: The field of "Pomeron" physics has been stimulated in recent years by the experimental studies for small-x physics at HERA as well as by "hard diffractive" measurements at FNAL; its import will become more prominent as one moves into the LHC energies, e.g., diffractive Higgs production. Prof. Tan has carried out several related projects in this area. Prof. Tan has examined carefully the notion of Pomeron flux and its renormalization. By maintaining factorization, unambiguous predictions for double Pomeron exchange, doubly diffraction dissociation, etc., both at Tevatron and at LHC energies, can be made. In view of our recent work, (hep-th/0603115), further refinement is currently being formulated. Another project involves an effort in providing a unified treatment of HE hadronic collision incorporating both hard and soft processes at high energy. Recently, progress has been achieved in a theoretical understanding of the structure of the soft Pomeron. The key idea of this picture is the observation that the scale for the soft Pomeron could be related to the violation of the scale anomaly of QCD. A consistent model was constructed which can provide a practical phenomenological framework for interpreting data from HERA to FNAL and beyond. Prof. Tan have been invited to discuss these subjects recently at the Blois meeting on Elastic and Diffraction and at International Symposium on Multiparticle Dynamics.
String/Flux-Tube Duality on the Lightcone: In collaboration with R. Brower and C. Thorn, Prof. Tan has also explored the equivalence of quantum field theory and string theory as exemplified by the AdS/CFT correspondence from the point of view of lightcone quantization. The postulate of quark confinement in QCD is usually associated with the idea that, in the theory without dynamical quarks, there is a mass gap mG (the lightest glueball mass) and the gauge field responds to a fixed quark source separated from a fixed antiquark source by a distance L >> mG-1 by forming some kind of gluonic flux tube between these sources, with the energy of the quark-antiquark system growing with L as U(L) ~ T0 L. One of the big surprises of the duality between superstring theory on AdS5xS5 and N=4 (supersymmetric Yang Mills) is that in the 't Hooft limit a string description can even be applied to a gauge theory that neither confines nor possesses a mass gap. The absence of a mass gap in this case has motivated those exploring the precise nature of the AdS/CFT correspondence to supply an IR cutoff by defining the field theory on S3 rather than R3. However there are some physical situations which provide their own infrared cutoff (when Nc? infinity), and these can be safely analyzed on R3. Among these is the case of fixed quark and antiquark sources separated by a distance L. Thus the large Nc limit of the quark-antiquark system can be explored in a well-defined way whether or not confinement occurs. In particular, perturbation theory applied to this system is infrared safe. Brower, Tan, and Thorn have carried out an investigation to see how the lightcone description deals with the many aspects of the duality already understood from other starting points, e.g., on the string side, they discuss the lightcone version of small oscillations about the static string connecting a heavy external quark source to a heavy external antiquark source. Their results are completely consistent with those obtained by more standard covariant methods , thus providing further support for the AdS/CFT conjecture.
Glueballs in an AdS Black Hole and Localized Gravity: As a further exploration of the AdS/CFT correspondence, Brower, Mathur and Tan considered a model of brane world gravity in the context of non-conformal non-SUSY matter in the confined phase. They modify the earlier strong coupling solution to the glueball spectrum in an AdS Black Hole by introducing a Randall-Sundrum Planck brane as a UV cut-off. The consequence is a new normalizable zero mass tensor state, which gives rise to an effective Einstein-Hilbert theory of gravity, with exponentially small corrections to the discrete glueball spectrum 11. The large mass hierarchy required for the effective 4-d Planck mass relative to the QCD scale is exponential in the proper distance from rmin to rc. The goal of this toy model is to exhibit a self-consistent model of gravity interacting with non-conformal matter in the confined phase. However the simplest microscopic theory for the Planck brane is found to have a tachyonic instability in the radion mode. A mechanism for stability is discussed. For AdS7 which exhibits a reasonable approximation to the known glueball spectrum of lattice simulations for QCD4, there is an additional flat compact dimension coming from the 11th direction of M-theory. This gives rise to a compactified 5-d brane world gravity with a Kaluza-Klein ``photon'' and ``dilaton''. In their earlier paper they had noted that the strong coupling glueball spectrum had an ``accidental'' scalar-tensor degeneracy. The same mechanism that is need to split this spectral line consistent with QCD at weak coupling here is apparently needed to lift the dilaton mass consistent with cosmological constraints.
Improved Treatment of Chiral Symmetry and Lattice QCD: A persistent difficulty with the standard lattice approach to low energy hadronic process is the inadequate characterization of the "pion cloud" due to the long extrapolation from unphysically massive u, d quarks. A related issue is the difficulty with small eigenvalues in the limit of small quark mass, which through the Banks-Cashir formula are responsible for chiral symmetry breaking. Since these eigenvalues are represented faithfully by bosonic matrix models, one might hope that they could somehow be ``bosonized''. Brower, Shen and Tan introduced a new methods called ``chirally extended QCD'' (or ?QCD) in this spirit. The lattice action is modified by adding explicit fields for the Goldstone modes that has the effect of replacing the low eigenvalues by a constituent quark mass, Mq, without explicitly breaking chiral symmetry. Brower, Edwards, Tan and Lim have recently extended the study of ?QCD to domain-wall and overlap fermions. It can be shown that it is possible to have exact SUL(Nf) x SUR(Nf) x UV(1) symmetry as a non-abelian generalization of the Ginsparg-Wilson relation, and the continuum limit for ?QCD on the lattice will approach the universal fixed point for QCD without fine-tuning. One approach is a direct generalization a chiral extension to QCD proposed previously, consistent with the Ginsparg-Wilson relation. A second approach, ibased on the Callan, Coleman, Wess and Zumino coset construction, allows extrapolating to a zero quark axial coupling, gA = 0 where the fermionic determinant is shown to be real. More details will be given in a forthcoming publication by R. Brower, R. Edwards, K-T Lim, and C-I Tan. This work also represents the PhD thesis of Kyung-Teak Lim, who completed his PhD requirements this year.
Confinement/Deconfinement Transitions: One of the original motivations for studying string thermodynamics was to model the confinement/deconfinement phase transition in QCD. With the advent of AdS/CFT, this subject has received renewed interest. It has been conjectured that string theory in a pp-wave background (BMN limit) is dual to a sector of N=4 supersymmetric Yang-Mills theory. Several recent papers have studied the Hagedorn transition for free strings in this background, leading to conflicting claims , which have since been resolved due to a systematic treatment by Brower, Lowe, and Tan. In order to isolate the subsector appropriate in the BMN limit, it is necessary to introduce, in addition to the inverse temperature, ?, a chemical potential, ?, for the longitudinal momentum, corresponding to the large R-charge limit of the gauge theory. This string background exhibits Hagedorn-like behavior. They show that the free energy has a square-root singularity in ?, F(?, ?; ?) ~ c (? - ?H(?;?))1/2 + regular part, and the Hagedorn temperature, TH= ?H-1, is a function of both the chemical potential ? and the mass parameter, ?. They find the free energy at the transition point is finite suggesting a confinement/deconfinement transition in the gauge theory. The mass parameter m effectively confines oscillations of strings in the transverse directions. In the limit that the curvature may be neglected (i.e. ? ? 0) they have found that all salient features are in fact already visible in the more familiar context of strings in a toroidal compactification, contrary to claims made by others. Interestingly, this system has been used in the past to model QCD at finite baryon number chemical potential. They also obtain a number of results not previously noted in the literature, e.g., the famous semi-circle law at finite chemical potential. A microcanonical analysis for such system has also been carried out. This can also be applied to the study for the onset of deconfinement transition, and work in this direction is currently underway in collaboration with Drs. D. Kharzeev and F. Karsch of BNL.
Honors and Awards
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Affiliations
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Funded Research
RESEARCH GRANTS:
(a) Current Grants:
(i) U. S. Department of Energy, "Theoretical Studies in High-Energy Physics", (Cont.
DOE-DE-FG02-91ER40688.A013 - Task A), Nov. 2005-Oct. 2006, Co-principal Investigator.
(ii) National Science Foundation, "Support for US HE Physics for Moriond Conf.",
03/15/06-04/14/07, Principal Investigator.
(b) Recently Completed Grants:
(i) U. S. Department of Energy, "Theoretical Studies in High-Energy Physics", (Cont.
DOE-DE-FG02-91ER40688.A013 - Task A), Nov. 2001-Oct. 2005, Co-principal Investigator.
(ii) National Science Foundation, "Support for US HE Physics for Moriond Conf.", 03/15/00-04/14/04, Principal Investigator.
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Curriculum Vitae
Read Chung-I Tan's full Faculty Research Profile.
