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# James Sparks

#### Professor James Sparks

## Interests and expertise (Subject groups)

## Grants awarded

#### Geometry and duality in string theory

#### Geometry and duality in string theory

#### Geometry and duality in string theory

#### Geometry and duality in string theory

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Research Fellow

**Scheme: **University Research Fellowship

**Organisation: **University of Oxford

**Dates: **Oct 2012-Sep 2015

**Value: **£273,212.44

**Summary: **One of the most important conceptual developments in theoretical physics in recent years is a conjecture known as the AdS/CFT correspondence. This states that quantum theories of gravity in certain spacetimes, called anti-de Sitter (AdS) spacetimes, may equivalently be described by a type of quantum field theory without gravity, called a conformal field theory (CFT). Such conjectured equivalences, relating two apparently different theoretical frameworks, are known as dualities. A remarkable feature of the AdS/CFT duality is that the CFT lives on the boundary of the region in which gravity propagates. The correspondence in particular implies that one can learn about quantum field theories by studying gravity, and vice versa. In practice, the AdS/CFT correspondence is understood best in the context of string theory.
My research over the last year has centred on the precise details of how this proposal works in string theory. Some of the spatial dimensions in which the strings move must be curled up into very specific shapes; but there are infinitely many allowed shapes, and each one should lead to a different CFT. I have been investigating the different spaces on which one can define these CFTs, and understanding their dual description in terms of solutions to Einstein's equations. In particular, I have uncovered a new class of physical quantities that may be computed exactly in both theoretical frameworks, giving new tests of the AdS/CFT conjecture. I have also been trying to understand the AdS/CFT correspondence when the strings are strongly interacting with each other, which is a limit of string theory known as M-theory. The AdS/CFT correspondence in this setting, as well as being of theoretical interest, also has potential applications to condensed matter physics.

**Scheme: **University Research Fellowship

**Organisation: **University of Oxford

**Dates: **Oct 2007-Sep 2012

**Value: **£458,904.20

**Summary: **One of the most important conceptual developments in theoretical physics in recent years is a conjecture known as the AdS/CFT correspondence. This states that quantum theories of gravity in certain spacetimes, called anti-de Sitter (AdS) spacetimes, may equivalently be described by a type of quantum field theory without gravity, called a conformal field theory (CFT). Such conjectured equivalences, relating two apparently different theoretical frameworks, are known as dualities. A remarkable feature of the AdS/CFT duality is that the CFT lives on the boundary of the region in which gravity propagates. The correspondence in particular implies that one can learn about quantum field theories by studying gravity, and vice versa. In practice, the AdS/CFT correspondence is understood best in the context of string theory.
My research over the last year has centred on the precise details of how this proposal works in string theory. Some of the spatial dimensions in which the strings move must be curled up into very specific shapes; but there are infinitely many allowed shapes, and each one should lead to a different CFT. I have been investigating the different spaces on which one can define these CFTs, and understanding their dual description in terms of solutions to Einstein's equations. In particular, I have uncovered a new class of physical quantities that may be computed exactly in both theoretical frameworks, giving new tests of the AdS/CFT conjecture. I have also been trying to understand the AdS/CFT correspondence when the strings are strongly interacting with each other, which is a limit of string theory known as M-theory. The AdS/CFT correspondence in this setting, as well as being of theoretical interest, also has potential applications to condensed matter physics.

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