Low-energy theorems and spectral density of the Dirac operator in AdS/QCD models

2009 ◽  
Vol 80 (12) ◽  
Author(s):  
P. N. Kopnin
Keyword(s):  
Dirac Operator ◽  
Spectral Density ◽  
Low Energy

scholarly journals EFFECTIVE LOW-ENERGY THEORIES AND QCD DIRAC SPECTRA

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1404-1415 ◽  
Author(s):  
D. TOUBLAN ◽  
J. J. M. VERBAARSCHOT
Keyword(s):  
Partition Function ◽  
Dirac Operator ◽  
Spectral Density ◽  
Random Matrix ◽  
Matrix Theory ◽  
Low Energy ◽  
Effective Theory ◽  
Kinetic Term ◽  
Dirac Spectrum ◽  
Energy Theory

We analyze the smallest Dirac eigenvalues by formulating an effective theory for the Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according to a Random Matrix Theory with the global symmetries of the QCD partition function. The kinetic term provides information on the slope of the average spectral density of the Dirac operator. In the second half of this lecture we interpret quenched QCD Dirac spectra (with eigenvalues scattered in the complex plane) in terms of an effective low energy theory.

ROLE OF THE ELECTRON–PHONON INTERACTION ON THE SPECTRAL DENSITY AND PSEUDOGAP IN CUPRATES

2002 ◽  
Vol 16 (23) ◽  
pp. 3465-3471
Author(s):  
I. CHAUDHURI ◽  
S. K. GHATAK
Keyword(s):  
Critical Temperature ◽  
Spectral Density ◽  
Low Energy ◽  
Phonon Interaction ◽  
Energy Excitation ◽  
Electron Phonon Interaction ◽  
Peak Structure ◽  
Electronic Model ◽  
Jahn Teller

The pseudogap structure in low energy excitation in cuprates appears below a temperature and the spectral density exhibits strong wave-vector dependence. An electronic model that emphasized the coupling of carrier in Cu-O with phonon is examined for pseudogap. The electron–phonon interaction originates from the modulation of on-site and hopping energy and leads to spontaneous Jahn–Teller-like distortion and pseudogap below a critical temperature. At low temperature the spectral density has two-peak structure about the Fermi level for all k along Γ-M whereas such structure exists along Γ-X for small k only. The magnitude of pseudogap shows strong k-dependence — maximum along Γ-M and vanishes along Γ-X. These features emphasize the role of electron–phonon interaction in formation of pseudogap.

scholarly journals STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4501-4517 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Low Energy ◽  
Target Space ◽  
World Sheet ◽  
Crucial Point ◽  
Spectral Action ◽  
Energy Eigenvalues ◽  
The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

scholarly journals Statistical properties of the spectrum of the QCD Dirac operator at low energy

2001 ◽  
Vol 603 (1-2) ◽  
pp. 343-368 ◽  
Author(s):  
D. Toublan ◽  
J.J.M. Verbaarschot
Keyword(s):  
Dirac Operator ◽  
Statistical Properties ◽  
Low Energy

scholarly journals Spectral density of the Dirac operator in two-flavor QCD

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
Georg P. Engel ◽  
Leonardo Giusti ◽  
Stefano Lottini ◽  
Rainer Sommer
Keyword(s):  
Dirac Operator ◽  
Spectral Density

scholarly journals Spectral density of the QCD Dirac operator near zero virtuality

1993 ◽  
Vol 70 (25) ◽  
pp. 3852-3855 ◽  
Author(s):  
J. J. M. Verbaarschot ◽  
I. Zahed
Keyword(s):  
Dirac Operator ◽  
Spectral Density
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