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Abhijnan Rej

Publications and source records attributed to Abhijnan Rej.

7 recordsLinked to original sources
arXiv2012

Ranks of gauge groups and an NP-complete problem on the Landscape

We prove that the problem of determination of factor gauge groups given the rank of the gauge group at any given vacuum in the Landscape is in the computational complexity class NPC. This extends a result of Denef and Douglas on the computational complexity of determination of the value of the cosmological constant in the Landscape.

math-ph↗
arXiv2012

Dimension, Divergence and Desingularization

I argue that consistent geometrical descriptions of the universe are far from unique even as low-energy limits and that an abstract "atomic" description of spacetime and gauge-theoretic geometry in terms of K-theories of algebraic and analytic cycles has the promise to restore uniqueness to our description.

gr-qc↗
arXiv2009

Motives: an introductory survey for physicists

We survey certain accessible aspects of Grothendieck's theory of motives in arithmetic algebraic geometry for mathematical physicists, focussing on areas that have recently found applications in quantum field theory. An appendix (by Matilde Marcolli) sketches further connections between motivic theory and theoretical physics.

hep-th↗
arXiv2009

Turing's Landscape: decidability, computability and complexity in string theory

I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the average rank of the (unification) gauge group in the Landscape, the explicit construction of Ricci-flat metrics on Calabi-Yau manifolds as well as the computability of fundamental periods to show that undecidability questions are far more pervasive than that described in the work of Denef and Douglas.

hep-th↗
arXiv2008

Supermanifolds from Feynman graphs

We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying a condition generalizing the log divergence in this context. The analog in this setting of the graph hypersurfaces is a graph supermanifold given by the divisor of zeros and poles of the Berezinian of a matrix associated to the graph, inside a superprojective space. We introduce a Grothendieck group for supermanifolds and we identify the subgroup generated by the graph supermanifolds. This can be seen as a general procedure to construct interesting classes of supermanifolds with associated periods.

hep-th↗