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### String Theory and M-Theory

Superstrings are widely thought to provide the basis for a unified theory of all of physics. Superstrings propagate in ten dimensions and yield a consistent perturbative quantum theory of gravity along with Yang-Mills gauge interactions. At low energy superstrings behave as particles and their low energy effective actions are the ten-dimensional supergravity theories. In the perturbative formulation of string theory, spacetime scattering amplitudes are computed using a conformal quantum field theory (CFT) living on the string world-sheet. The lightest modes of these strings give rise to gravity and gauge forces but strings also include an infinite tower of massive modes. As such the familiar geometrical notion of spacetime is not built into the theory from the start but is derived from its low-energy spectrum. However we now know that the notions of particles and strings should be generalised to include other higher-dimensional extended objects known as branes. Furthermore there is a deeper underlying theory, known as M-theory, whose microscopic dynamics is as yet unknown but which unifies the various string theories and contains M2-branes and M5-branes but no particles or strings.

### Branes and AdS/CFT

In String Theory D-branes, which are the end points of open strings, are dynamical and their low energy actions are given by Yang-Mills gauge theories coupled to matter. Such theories are of great interest in physics, for example they underlie the Standard Model of Particle Physics. In M-theory we lack a microscopic description. For M2-branes the low energy theory is given by three-dimensional Chern-Simons gauge theories with matter but for M5-branes M-theory predicts new and to-date ill-understood CFT’s in six-dimensions. String/M-Theory techniques have led to a great deal of progress in understanding these non-trivial theories. Surely the most striking development is a precise correspondence between the gauge theory of a large number of branes and a complete quantum gravity theory of String or M-Theory in certain asymptotically Anti-de-Sitter (AdS) spacetimes. This is known as the AdS/CFT correspondence and features heavily in modern research, including applications to more real world, experimentally accessible physics.

### Conformal field theory

In String Theory D-branes, which are the end points of open strings, are dynamical and their low energy actions are given by Yang-Mills gauge theories coupled to matter. Such theories are of great interest in physics, for example they underlie the Standard Model of Particle Physics. In M-theory we lack a microscopic description. For M2-branes the low energy theory is given by three-dimensional Chern-Simons gauge theories with matter but for M5-branes M-theory predicts new and to-date ill-understood CFT’s in six-dimensions. String/M-Theory techniques have led to a great deal of progress in understanding these non-trivial theories. Surely the most striking development is a precise correspondence between the gauge theory of a large number of branes and a complete quantum gravity theory of String or M-Theory in certain asymptotically Anti-de-Sitter (AdS) spacetimes. This is known as the AdS/CFT correspondence and features heavily in modern research, including applications to more real world, experimentally accessible physics.

### Statistical Physics and Integrability

Statistical physics is the science of emergent behaviours in many-body systems. For example consider the large reduction of the number of parameters that are used to describe thermodynamic equilibrium. But there is much more. For instance quantum field theory describes the universal, large-distance correlations and fluctuations near second-order phase transitions. Hydrodynamics is another universal framework. Out of equilibrium, new correlations emerge in particular due to the hydrodynamic modes, and hydrodynamics is a powerful theory for the motion and correlations at large spacetime scales. Strong results in statistical physics can be obtained in integrable systems, which admit enough symmetries so as bring out a rich mathematical structure and enable exact solutions. The Group is also very active in statistical physics and integrability. This includes integrable systems, conformal field theories and quantum chains. Of particular interest is their mathematical structure, entanglement properties as well as their applications to gauge theory, condensed matter physics, hydrodynamics and non-equilibrium physics.

### Defects in topological and conformal field theory 2019

Defects in topological and conformal field theory (27-28 June, 2019) an international workshop with speakers from seven countries meeting to recent developments in the theory of defects in conformal and topological field theories, sponsored by the London Mathematical Society and the Mathematical and Theoretical Physics group of the institute of Physics.

Defects 2019

### 13th South East Mathematical Physics Seminar

The department is a member of the South East Mathematical Physics Seminar network and hosts regular one-day meetings bringing together members from universities across the South East of the UK. The most recent held in King's was on 21 Feb, 2019, following on from previous meetings in 2017 and 2014.

SEMPS13

### 23rd European String Workshop: Strings, Geometry and Black Holes

The Mathematics department hosted the 23rd European String Workshop in April 2018, entitled Strings, Geometry, and Black Holes. This was an international conference with about 190 participants, and was supported by Imperial College London, King's College London, and the University of Oxford. It focussed on various aspects of string theory, gauge-gravity duality, black holes, quantum field theory, supersymmetry and the diverse connections with geometry.

23rd European String Workshop

### String Theory in London 2016

The Mathematics department hosted a conference in the period 29 August - 3 September 2016, entitled String Theory in London 2016: Supersymmetry, Geometry, and Holography. This was an international conference with about 90 participants which focussed on latest developments in various aspects of string theory.

### ICFT 2016 - UK Meeting on Integrable and Conformal Field Theory

The UK Meeting on Integrable and Conformal Field Theory is an annual event, started at King's in 1997 and held around the UK every year since then, returning to King's in 2001, 2007 and most recently in 2016. This brings together the UK community in integrable and conformal field theory with international speakers to discuss the recent developments in this field. In 2016, it was sponsored by the London Mathematical Society and the Mathematical and Theoretical Physics group of the institute of Physics.

ICFT2016

### Mathematical Physics of Non-Equilibrium Quantum Systems

Mathematical Physics of Non-Equilibrium Quantum Systems (18-19 December 2014): an international conference on the techniques and ideas underlying non-equilibrium quantum systems, co-hosted with the Department of Physics. This was a group event of the Theoretical and Mathematical Physics Group of the Institute of Physics, a Focus Workshop of the EPSRC Network Plus on Emergence and Physics far from Equilibrium, and was co-sponsored by the EPSRC Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES).

### Entanglement Entropy in Many Body Quantum Systems

"Entanglement Entropy in Many Body Quantum Systems" (2-4 June 2014): an international conference on entanglement entropy and related aspects in many body quantum systems, co-hosted with City University.

### One day meeting in honour of Peter West FRS

11 June 2013, a one day meeting of pedagogical talks in honour of Peter West FRS.

### Maths of String and Gauge Theory

Maths of String and Gauge Theory - 3 - 5 May 2012, an international conference on the mathematics of string and gauge theory hosting over 70 researchers. This event was co-hosted with City University.

### LMS pre-meeting

LMS pre-meeting - Friday, 21 November 2008, a meeting for graduate students in advance of the main meeting in the late afternoon.

### FPUK 2

FPUK 2, a two day workshop on fundamental physics, 7-8 November 2008

### FPUK 1.0

FPUK 1.0, a two day workshop on fundamental physics, 8-9 November 2007

### 11th Annual UK meeting on Integrable Models, Conformal Field Theory and Related Topics

ICFT07, the 11th Annual UK meeting on Integrable Models, Conformal Field Theory and Related Topics, 11-12 May 2007.

### Modern Developments in General Relativity and their Historical Roots