Supersymmetric color superconductivity Page: 4 of 29
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
U(1)B
Broken Trivially
U(l)B
Broken Dynamically g
U(l)B Unbroken
mU(l)B
Broken Trivially U(l)B
Broken Dynamically
,' U(l)B Unbroken
mFigure 1: Schematic phase diagrams in the p-m plane where m is the supersymmetric
mass. The diagram on the left shows the situation for Nf = N, and the diagram on the
right shows the situation for N, + 1 < Nf < 2N,. The dashed line is the critical chemical
potential. These diagrams are only valid for p < A.
we adapt this formalism to SQCD. In Sections 4-7 we determine the global symmetries of
SQCD with various numbers of flavors, and in Section 8 we conclude. Appendix A contains
a simple and explicit example in quantum mechanics, as a check on the method of including
a chemical potential, while Appendix B reviews the exact results for soft masses in SUSY
theories.
2 Relativistic Bose-Einstein Condensation
Let us begin by reviewing the relativistic formulation of Bose-Einstein condensation for a
non-supersymmetric scalar field theory. A nice description is given in [8, 9]. There are two
purposes to this discussion. One is to show that we can regard the chemical potential as the
time component of a fictitious gauge field of the U(1)B symmetry at zero temperature. The
other is to find the criterion for the U(1)B not to be immediately broken in the presence
of a chemical potential so we can study the dynamical breakdown.
The partition function in the grand canonical ensemble with nonzero chemical potential
can be calculated using the following path integral:
Z = Tr e-3(H-gN)C DirtDir D4tD e d fx a]
(1)
where A is the time-component of some conserved current. We consider the case of a
complex scalar field, where the Hamiltonian is' = 7rir + Vo - V# + m2 t
(2)
and the conserved current is J, = i(4t&N,4-#b,4t). Thus AV = i(#tirt -0ir). The integrand
of the exponent in the path integral can be rewritteni (rta'ot + 0r,0#)
(7rtTr + Vat . v# + rn2ot ) + ip (7rti
3
~
7r#)
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Harnik, Roni; Larson, Daniel T. & Murayama, Hitoshi. Supersymmetric color superconductivity, article, September 18, 2003; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc780044/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.