In this review article, we discuss the distinction and possible equivalence between scale
invariance and conformal invariance in relativistic quantum field theories. Under some …

The complex singularity exponent is a local invariant of a holomorphic function determined
by the integrability of fractional powers of the function. The log canonical thresholds of …

For 3-dimensional field theories with\(\mathcal {N}= 2\) supersymmetry the Euclidean path
integrals on the three-sphere can be calculated using the method of localization; they …

Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate
relationship between Sasakian and Kähler geometries, especially when the Kähler structure …

We develop a systematic and efficient method of counting single-trace and multi-trace BPS
operators with two supercharges, for world-volume gauge theories of N D-brane probes for …

We discuss the theory of equivariant localization focussing on applications relevant for
holography. We consider geometries comprising compact and non-compact toric orbifolds …

In this paper we study compact Sasaki manifolds in view of transverse Kähler geometry and
extend some results in Kähler geometry to Sasaki manifolds. In particular we define integral …

arXiv:1004.2461v2 [math.DG] 24 May 2010 Page 1 arXiv:1004.2461v2 [math.DG] 24 May
2010 Sasaki-Einstein Manifolds James Sparks A Sasaki-Einstein manifold is a Riemannian …

One of the general strategies for realizing a wide class of interacting QFTs is via junctions
and intersections of higher-dimensional bulk theories. In the context of string/M-theory, this …

Can artificial intelligence learn mathematics? The question is at the heart of this original
monograph bringing together theoretical physics, modern geometry, and data science. The …