Non-commutative Geometry and Emergent Gravity

• Grant number: 13/17765-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2014
• End date: August 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Victor de Oliveira Rivelles
• Grantee: Raju Roychowdhury
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

My research plan encompasses Non-commutative geometry and emergent gravity and is aimed at the ultimate unification between matter and geometry. The trinity of instantons namely between NC U(1) instantons, gravitational instantons and SU(2) Yang-Mills instantons may pave the path for such a novel unification scheme. A better understanding of the integrable systems in 4 dimension may be useful in the sense that, self dual 2 forms can be defined only in 4 dimensions and all physical forces eg. electromagnetic force, strong and weak force and gravitational force are represented by 2 forms on some orientable manifolds. According to Ward conjecture, self-dual systems in d=4 is the parent theory of (all) integrable systems in lower dimensions for eg. Hitchin systems in 2d, KdV etc. According to a theorem by Hitchin any hyperkahler manifold (kaher and Ricci flat) has one-to-one correspondence with a twistor space, so twistor space descriptions of instantons are also worth pursuing topics. Matrix model descriptions of gravitational instantons (which are hyper kahler manifolds) will lead to background independent theory of quantum gravity and emergent concept of spacetime will be a key concept in this framework. A better understanding of integrable systems or twistor space construction in terms of ADHM prescription is also an important subject for further study.

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CRUZ MORALES, JOHN ALEXANDER; MOVASATI, HOSSEIN; NIKDELAN, YOUNES; ROYCHOWDHURY, RAJU; TORRES, MARCUS A. C.. Manifold Ways to Darboux-Halphen System. Symmetry Integrability and Geometry-Methods and Applications, v. 14, 2018. (13/17765-0)

CHANDA, SUMANTO; GUHA, PARTHA; ROYCHOWDHURY, RAJU. Schwarzschild instanton in emergent gravity. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, v. 14, n. 1, JAN 2017. (13/17765-0)

CHANDA, SUMANTO; GUHA, PARTHA; ROYCHOWDHURY, RAJU. Bianchi-IX, Darboux-Halphen and Chazy-Ramanujan. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, v. 13, n. 4, APR 2016. (13/17765-0)

CHANDA, SUMANTO; GUHA, PARTHA; ROYCHOWDHURY, RAJU. TAUB-NUT AS BERTRAND SPACETIME WITH MAGNETIC FIELDS. JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, v. 41, p. 33-67, 2016. (13/17765-0)

GUPTA, SAURABH; ROYCHOWDHURY, RAJU. Antiself-dual Yang-Mills, modified Faddeev-Jackiw formalism and hidden BRS invariance. International Journal of Modern Physics A, v. 31, n. 24, AUG 30 2016. (13/17765-0)