# String Theory Group Research

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**Phenomenological Consequences of String Theory**

Emilian Dudas, Hervé Partouche

The standard model of particle physics describes all known elementary particles and their interactions and provides a unified description of electromagnetism and the strong and weak nuclear forces. Despite its success in particle physics it cannot be a complete description of nature because it fails to incorporate gravity and leaves unanswered several questions such as the hierarchy problem. String theory is a framework that replaces the point-like particles of quantum field theory by extended objects - strings - and predicts the graviton as one of its vibrational modes. Consistency of the theory requires a new symmetry between bosons and fermions called supersymmetry, and the existence of extra dimensions. Compactification of these dimensions in the presence of fluxes gives rise to a landscape of string theory vacua which result in semi-realistic models of particle physics once supersymmetry has been broken. Understanding the mechanisms for supersymmetry breaking and constructing complete (meta)stable four-dimensional particle physics models are among the major challenges. A particularly important yet difficult problem is that of finding de Sitter vacua in string theory as relevant for describing the expansion of the universe. Currently the leading theory going beyond the Big Bang is the theory of cosmic inflation. Important open problems consist in understanding the string origin of the cosmological constant and the transitions occurring during the cosmological evolution.

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**Mathematical Aspects of String Theory**

Guillaume Bossard, Marios Petropoulos

The quantum gravity regime of string theory, in which stringy excitations and Kaluza-Klein states are negligible while the Newton constant remains finite, is always at strong string coupling. It is therefore important to understand non-perturbative corrections in string theory to study quantum gravity at low energy. Vacua of string theory with extended supersymmetry are not phenomenologically realistic, but allow to use extremely powerful tools to simplify computations. Amplitudes in supergravity and string theory with extended supersymmetry can in particular be computed at rather high loop order. Combining knowledge from supergravity / string amplitudes, non-perturbative symmetries in string theory and supersymmetry, one can sometimes compute exact couplings. These exact couplings carry valuable informations about non-perturbative states in the theory, and in particular about BPS black hole micro-states. This connects to the mathematics of automorphic representations, generalized geometry and Kac-Moody algebras. These problems are naturally formulated in the framework of exceptional field theory, which defines a unifying theory for higher dimensional supergravity theories, gauged supergravities, and includes non-perturbative BPS states.

## Gauge-gravity duality: fundamentals, applications and extensions

Blaise Goutéraux, Marios Petropoulos, Andrea Puhm

The realization that quantum gravity in Anti de Sitter (AdS) spacetime may be described by a Conformal Field Theory (CFT) living at its boundary has opened a new window into studying a variety of physical phenomena through so-called gauge-gravity dualities (or, more colloquially, holography). Major successes of the original duality, the AdS/CFT correspondence, include an interpretation of the Bekenstein-Hawking entropy of extremal black holes in AdS space as an ensemble of microstates in the dual conformal field theory, and a lower bound on the ratio of the shear viscosity over entropy density of strongly-coupled plasmas from a gravitational calculation of graviton absorption cross sections by near-extremal black branes.

Holography provides a powerful toolkit for studying strongly coupled quantum field theories. In the long-wavelength limit of AdS-CFT (known as fluid-gravity correspondence), a beautiful connection arises between two of the best-studied nonlinear partial differential equations in physics: the equations of hydrodynamics and the field equations of gravity. In recent years, this observation has been used to write down effective field theories, such as hydrodynamics, for systems with various patterns of broken symmetries, including plasmas, superconductors and charge density waves. These effective theories can then be applied to strongly-correlated condensed matter systems, such as high temperature superconductors and other bad metals, where the weakly-coupled quasiparticle paradigm breaks down.

Attempts to extend holography to non-AdS spacetimes such as asymptotically flat or de Sitter spacetimes is currently a topic of intense research. In particular, the Bondi-Metzner-Sachs (BMS) group and its enhancement to a Virasoro asymptotic symmetry group suggest the existence of a 2d "celestial" CFT living at the conformal boundary of 4d asymptotically flat spacetime. Its properties are currently inferred via a bottom-up approach by studying so-called celestial amplitudes, obtained by a change of basis of the asymptotic states in 4d scattering amplitudes, which share conformal properties with 2d correlation functions on the celestial sphere.

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**Black Holes and Quantum Gravity**

Guillaume Bossard, Marios Petropoulos, Andrea Puhm

An important aspect in formulating a theory of quantum gravity is the choice of boundary conditions and the resulting asymptotic symmetries of the spacetime. In asymptotically AdS spacetime the asymptotic symmetries are identified with those of a conformal field theory on the boundary of AdS which offers a non-perturbative formulation of string theory in AdS space. In asymptotically flat spacetimes the BMS group, an infinite-dimensional extension of the Poincare group of special relativity, plays an important role but a complete understanding of the infrared properties of quantum gravity is outstanding.

Understanding its ultraviolet behavior becomes particularly challenging when black holes are added to the picture. Black holes are objects in general relativity which are known to have a vast entropy, but when quantum mechanics is applied they evaporate by emission of Hawking radiation which carries no information about their microstates - this is the black hole information loss paradox which has evaded a resolution for over 40 years. String theory and the holographic AdS-CFT duality have offered indirect evidence that black holes are quantum mechanical systems that do not destroy information. However, to fully resolve Hawking's paradox requires extending the scope of these arguments beyond highly charged and/or spinning black holes and to explain the microscopic gravitational dynamics near the horizon. The fuzzball programme is an attempt to describe the microstates of a black hole by horizon-scale microstructure in string theory and suggests that the black hole geometry arises as a coarse-grained description of a large ensemble of microstates. It is an open question whether astrophysical black holes can be described by fuzzballs, or whether an effective black hole interior emerges for infalling observers.