# The Phase diagram of QCD

## Lecture 1: Thermodynamics and lattice gauge theory

Here are some notes on thermodynamics; this part of the lecture followed these notes. It would be useful also to read the article Thermodynamics, by , in the book Phase Transitions and Critical Phenomena, vol 2, edited by (publishers: Academic Press, 1972).

Any introductory book on lattice gauge theory would cover the material that was lectured upon. For a heavy-ion physicist, the points of interest here are the kind of uncertainties, ie, systematic errors, that exist in lattice computations, and how to compare results from different groups.

Gzipped pdf file of the lecture

## Lecture 2: The Phase diagram of QCD

This lecture gave an overview of the phase diagram of QCD, and included the main qualitative conjectures and the current lattice results. Here are the major references.

- Color Superconductivity and Chiral Symmetry Restoration at Nonzero Baryon Density and Temperature, J. Berges and K. Rajagopal, Nucl. Phys., B 538 (1999) 215. [arxiv]
- On the Phase Diagram of QCD, M. A. Halasz et al., Phys. Rev., D 58 (1998) 096007. [arxiv]
- Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point, M. A. Stephanov, K. Rajagopal and E. V. Shuryak, Phys. Rev., D 60 (1999) 114028. [arxiv]
- Signatures of the Tricritical Point in QCD, M. A. Stephanov, K. Rajagopal and E. Shuryak, Phys. Rev. Lett., 81 (1998) 4816.
- The chiral critical line of N_f=2+1 QCD at zero and non-zero baryon density, Ph. de Forcrand and O. Philipsen, J. H. E. P., 0701 (2007) 077. [arxiv] [arxiv]
- Lattice determination of the critical point of QCD at finite T and mu, Z. Fodor and S. Katz, J. H. E. P., 0203 (2002) 014. [arxiv]
- Critical point of QCD at finite T and mu, lattice results for physical quark masses, Z. Fodor and S. Katz, J. H. E. P., 0404 (2004) 050. [arxiv]
- The QCD thermal phase transition in the presence of a small chemical potential, C. R. Allton et al., Phys. Rev., D 66 (2002) 074507. [arxiv]
- Finite density QCD via imaginary chemical potential, M.-P. Lombardo and M. d'Elia, Phys. Rev., D 67 (2003) 014505. [arxiv]
- On the existence of a phase transition for QCD with three light quarks , F.-R. Brown et al., Phys. Rev. Lett., 65 (1990) 2491. [journal]
- The QCD phase diagram for small densities from imaginary chemical potential, Ph. de Forcrand and O. Philipsen, Nucl. Phys., B 642 (2002) 290. [arxiv]
- Pressure and non-linear susceptibilities in QCD at finite chemical potentials, R. V. Gavai and S. Gupta, Phys. Rev., D 68 (2003) 034506. [arxiv]
- The critical end point of QCD, R. V. Gavai and S. Gupta, Phys. Rev. D 71 (2005) 114014 [arxiv]
- QCD at finite isospin density, D. T. Son and M. A. Stephanov, Phys. Rev. Lett., 86 (2001) 592. [arxiv]
- The Equation of State for Two Flavor QCD at Non-zero Chemical Potential, C. R. Allton, et al., Phys. Rev., D 68 (2003) 014507. [arxiv]
- The equation of state in lattice QCD: with physical quark masses towards the continuum limit, Y. Aoki, et al., Phys. Lett., B 643 (2006) 46. [arxiv]
- Study of the finite temperature transition in 3-flavor QCD using the R and RHMC algorithms, M. Cheng et al., Phys. Rev., D 75 (2007) 034506. [arxiv]

Gzipped ppt file of the lecture

## Lectures 3 and 4: Properties of QCD matter

This part of the lectures concentrated on properties of QCD matter as found on the lattice and otherwise. Indispensable primary references are Statistical Mechanics and Fluid Dynamics by . The list of references for QCD matter is really large (and rap[idly growing), and it is not feasible to list them in their entirety. However, here are some which directly deal with material covered in the lectures and also point to other references.

- The speed of sound and specific heat in the QCD plasma: hydrodynamics, fluctuations and conformal symmetry, R. V. Gavai, S. Gupta and S. Mukherjee, Phys. Rev. D 71 (2005) 074013 [arxiv]
- The equation of state for two flavor QCD at N_t=6, C. Bernard et al., Phys. Rev., D 55 (1997) 6861 [arxiv]
- Thermodynamics of SU(3) Lattice Gauge Theory, J. Engels et al., Phys. Lett., B 396 (1997) 210 [arxiv]
- The Pressure in 2, 2+1 and 3 Flavour QCD, F. Karsch, E. Laermann and A. Peikert, Phys. Lett., B 478 (2000) 447 [arxiv]
- Equation of state in finite-temperature QCD with two flavors of improved Wilson quarks, A. Ali Khan et al., Phys. Rev., D 64 (2001) 074510 [arxiv]
- Fluctuations, strangeness and quasi-quarks in heavy-ion collisions from lattice QCD, R. V. Gavai and S. Gupta, Phys. Rev. D 73 (2006) 014004 [arxiv]
- QCD equation of state with 2+1 flavors of improved staggered quarks, C. Bernard et al., Phys. Rev., D 75 (2007) 094505 [arxiv]
- A Calculation of the shear viscosity in SU(3) gluodynamics, H. B. Meyer, arXiv:0704.1801 [hep-lat]. [arxiv]
- The Bulk Viscosity of High-Temperature QCD, P. Arnold, C. Dogan and G. D. Moore, Phys. Rev., D 74 (2006) 085021. [arxiv]
- Bulk viscosity of QCD matter near the critical temperature, D. Kharzeev and K. Tuchin, arXiv:0705.4280 [hep-ph]. [arxiv]
- The Electrical conductivity and soft photon emissivity of the QCD plasma, S. Gupta, Phys. Lett., B 597 (2004) 57. [arxiv]
- Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, D. T. Son and A. O. Starinets, J. H. E. P., 209 (2002) 042. [arxiv]
- Dynamic universality class of the QCD critical point, D. T. Son and M. A. Stephanov, Phys. Rev., D 70 (2004) 056001. [arxiv]
- Phenomenological approach to the critical dynamics of the QCD phase transition revisited, T. Koide, J. Phys., G 31 (2005) 1055. [arxiv]

Gzipped pdf file of lecture 3 and gzipped pdf file of lecture 4

© Sourendu Gupta