Home » Lectures » Bobby Acharya: Lectures

Bobby Acharya: Lectures

May 14, 2024
TITLE: Confinement from Special Holonomy Cones

ABSTRACT: Explaining the properties of confinement and mass gap of Yang-Mills theory in four dimensions is one of the most important questions in physics over the past 50 years and would provide a deep insight into why quarks and gluons form bound states like protons and neutrons. Conical and asymptotically conical G2 and SU(3) holonomy spaces give rise to quantum field theories in four and five dimensions. We explain how confinement arises from asymptotically conical (AC) manifolds with a finite fundamental group whilst the mass gap occurs when certain L2-cohomology groups vanish. The main new result predicts confined, massive phases of quantum field theories in five dimensions which arise from certain AC Calabi-Yau threefolds.

September 7, 2023
TITLE: M-theory, particle physics and special singularities of special holonomy spaces: Past, Present and Future

ABSTRACT: Ricci flat spaces of special holonomy with special kinds of singularities provide models for the extra dimensions of physical space predicted by superstring/M-theory. After reviewing the intimate relationship between the singularities of these spaces and particle physics in four dimensions I will review some of the physics progress made by this Simons collaboration. Then I will review recent work (together with Daniel Baldwin) interpreting (a generalized version of) the Joyce-Karigiannis constructions of G2-manifolds in terms of Higgs and Coulomb phases of four dimensional gauge theories.

I will conclude with some perspectives on the future and some of the important open problems.

Marcb 17, 2023
TITLE: Progress and open problems in the physics of special holonomy spaces

Slides of Lecture

September 9, 2021
TITLE: The Physics of Some G2 and SU(3) Holonomy Singularities

ABSTRACT: After a brief survey of what is known about the physical interpretation of various kinds of singularities in special holonomy spaces, we describe some recent progress in understanding the physics of some classes of non-Abelian orbifold singularities and asymptotically conical G2 and SU(3) holonomy spaces. We expect that some of the G2 examples can be desingularised to give rise to new, complete G2-holonomy manifolds.

Slides of Lecture

September 14, 2020
TITLE: New G2-manifolds and Their Field Theory Interpretations

Slides of Lecture

September 12, 2019
TITLE: Some recent progress in the Physics of Special Holonomy Spaces: Dark matter, Gauge theories and The String Landscape

ABSTRACT: Acharya will survey recent progress in understanding the physics of special holonomy spaces as models for the extra dimensions of space in string/M theory. He will begin by briefly reviewing how special holonomy spaces can aid our understanding of particle physics and cosmology and how recent progress may help shape our picture of the dark sector of the universe. The talk will then go on to apply recent progress on the construction of a class of G2-holonomy spaces as circle bundles over Calabi-Yau’s (Foscolo, Haskins, Nordstrom) to M theory/Type IIA duality and, in particular, to four-dimensional gauge theories. Finally Acharya surveys some recent progress in physics related to the conjecture “stable, compact Ricci flat manifolds have special holonomy” and how it can shape our understanding of the String Landscape.
Slides of lecture

April 8, 2019
TITLE: New Local G2 Holonomy Spaces and their Gauge Theory Interpretations

Slides of lecture

September 13, 2018
TITLE: Supersymmetry, Special Holonomy, Ricci Flatness and the String Landscape

ABSTRACT: The main reason that physicists have been interested in Ricci flat spaces with special holonomy is supersymmetry. These spaces then lead to supersymmetric physical models defined on Minkowski spaces, primarily because the manifolds admit parallel spinors with respect to the Levi-Cevita connection. The rich relation between physics and mathematics has led to many significant results like mirror symmetry, Gromov-Witten theory, Donaldson-Thomas invariants and Gopakumar-Vafa, which leads one to suspect that special holonomy, Ricci flat manifolds are rather special objects. I will discuss the possibility that, perhaps all compact, simply connected, stable Ricci flat manifolds have special holonomy (i.e., the conjecture that could bear the slogan “supersymmetry equals Ricci flat equals special holonomy”).

I survey some of what is known about this question and discuss obstructions to the existence of Ricci flat metrics with generic holonomy, presenting some classes/constructions of manifolds which cannot admit a Ricci flat metric with generic holonomy. In dimension four, one of the main open questions is: Does S² ✕ S² admit a stable Ricci flat metric? I finish by discussing an instability in string theory that occurs for non-supersymmetric Ricci flat manifolds with finite fundamental group without parallel spinors (e.g. the Enriques surface) and suggest a connection to Witten’s `bubble of nothing.’

If the conjecture were true, it would strongly suggest that the only consistent theories of gravity in Minkowski spacetime are supersymmetric theories.

Slides of lecture

January 12, 2018
TITLE: String dualities and calibrated cycles

September 11, 2017
TITLE: M-theory/heterotic/type IIA duality

Slides of lecture

June 6, 2017
TITLE: M-theorists’ fantasy shopping list for singular G2 manifolds

Slides of lecture

January 9, 2017
TITLE: M theory and Type IIA superstring theory: Six-dimensional limits of G2 Manifolds

ABSTRACT: M theory spacetimes which are “fibered” by a circle have an alternative description in Type IIA
superstring theory in the limit that the circle is small. Supersymmetry in Type IIA theory leads to
spacetimes that are “Calabi-Yau threefolds with anti-holomorphic involutions together with special Lagrangian
D-branes and magnetic flux”. M theory/Type IIA duality requires that these arise as S1 collapsed limits of holonomy
G_2-manifolds. I will try and review this picture and emphasise the many open mathematical problems. Time permitting,
I will also discuss how “open Gromov-Witten theory” could be related to associative sub manifolds in M theory.

September 15, 2016
TITLE: Codimension seven singularities in M-theory compactifications

Slides of lecture

September 15, 2016
TITLE: Beyond the standard model

Slides of lecture

September 13, 2016
TITLE: The Standard model of particle physics

Slides of lecture

September 12, 2016
TITLE: Particle physics for mathematicians

Slides of lecture

September 6, 2016
TITLE: G₂-manifolds and Particle Physics

ABSTRACT: G_2-holonomy spaces serve as well motivated models of the seven extra dimensions of space predicted by M-theory. I will review how this leads to a completely geometric picture of all the known elementary forces including gravity. Special kinds of singularity of G_2-spaces play a crucial role in this picture, which one might regard as a generalisation of the McKay correspondence. I will try to describe some mathematical problems which have arisen from this work concerning the existence of G_2-holonomy metrics with singularities and questions about the moduli space of G_2-manifolds.

Slides of lecture