IFCPAR AR (ENGLISH) for CD - CEFIPRA

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Pure and Applied Physics
Dr. Kumar Sankar Gupta
Saha Institute of Nuclear Physics
Kolkata
Dr. Xavier Martin
Laboratoire de Mathématiques et
Physique Théorique de l’Université de
Tours
Faculté des Sciences et Techniques
Tours
Project 4004-1
FUZZY APPROACH TO QUANTUM FIELD THEORY
AND GRAVITY
IFCPAR
Indo-French Centre for the Promotion of Advanced Research
Duration: Three years (July, 2009 to June, 2012)
Objectives
i) Fuzzy physics, which is an offshoot of studies in
noncommutative geometry, provides an alternative method
to lattice methods for regularising and simulating quantum
field theory and quantum aspects of gravity which preserves
the symmetries of the underlying space
ii) It is proposed to explore in depth the scalar and gauge field
theories with a more efficient numerical scheme than
previous studies. It is also planned to analyze and simulate
supersymmetric and fermionic theories
iii) Finally, some simple noncommutative gravity models will
be studied using both analytical and numerical techniques,
concentrating on the fuzzy analogue of the BTZ black hole
and the corresponding AdS/CFT relations
Accomplishments
i) Efficient program was written to simulate the scalar field on
the fuzzy sphere using both the overrelaxation and heat
bath methods. New, non-rotationnally invariant,
observables for the field has been calculated
ii) "Fuzzified" the noncommutative cylinder. This will allow a
numerical investigation of the properties of the horizon of a
noncommutative black hole which has this geometry
iii) Discussed a numerical approximation of the fermionic field
beyond the quenched approximation using the symmetries
of the fuzzy sphere
iv) Simulated the scalar field on the fuzzy sphere finding the
field configurations in the non-uniform phase and looking
for "striped phases" there
v) Simulated the scalar field on the fuzzy cylinder to get the
phase diagram
Research papers published: Nil