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Content

# Scientific Program

*VIII Avogadro Meeting on String Theory, Supergravity and Gauge Theories
Scuola Normale Superiore – Aula Bianchi
December 19 – 21 2012*

## Wednesday, December 19 - Aula Bianchi

8.50 - 9.00 Opening

9.00 - 11,00 **
Valentina Giangreco Marotta Puletti** (Chalmers University of Technology, Sweden)

**Alberto Salvio**(Universidad Autónoma de Madrid, Spain)

*Holographic states of matter: from superconductors to strange metals*

### Abstract and references

**Abstract**

These lectures are meant to be an introduction to some topics in the Anti de Sitter/condensed matter theory correspondence. In the first part we will discuss holographic models for superconductors. We will first use effective field theories to introduce superconductivity and superfluidity in a model independent way, which will allow us to identify predictions of holography. We will then focus on holographic models at finite temperature *T* and chemical potential *μ* and having in the spectrum a charged scalar operator: the simplest realization of holographic superconductors. Some observables will be discussed, such as the conductivity, both in the normal and superfluid phases. While for homogeneous configurations superconductivity and superfluidity can be essentially identified as there is a mapping between the two, for non-homogeneous configuration they are physically different: The *U(1)* symmetry is global for superfluids and gauged for superconductors. We will discuss in detail this point and how a dynamical gauge field can be described holographically. The second part is devoted to holographic metals, in particular we will focus on (2+1)-dimensional systems of fermions at finite μ and at very low *T*. These systems show "strange" metallic phases (non-Fermi liquids). First, we will briefly review some key concepts in condensed matter physics in order to introduce the motivations and to understand the topics: the concept of Fermi surface, the modern RG approach to Fermi liquid theory, the concept of quantum critical points and the break-down of the Fermi liquid theory. Second, we will discuss the main holographic models proposed so far in order to holographically realize Fermi surfaces: We will introduce the Lifshitz scaling symmetry, the classification in mesonic and fractionalized phases, and some basic tools to holographically detect signals of Fermi surfaces.

- General useful reviews on AdS/CMT and first works on holographic superconductors:

McGreevy's review: http://arxiv.org/pdf/0909.0518

Hartnoll's review: http://arxiv.org/abs/arXiv:0903.3246

Herzog's review: http://arxiv.org/abs/0904.1975 - Introduction. motivations for holographic superconductors and metals:

cuprate phase diagrams, etc (http://arxiv.org/abs/cond-mat/0410445) - Part 1. Holographic superconductor.
- effective field theory methods for superfluids and superconductors (http://ptp.ipap.jp/link?PTPS/86/43/ and section 2 of http://arxiv.org/abs/arXiv:1005.1776)
- holographic superfluid phase transition and conductivity in the (un)broken phase (http://arxiv.org/abs/arXiv:0803.3295)
- dynamical (electro magnetic) fields in holographic superconductors (section 3.1 of http://arxiv.org/abs/arXiv:1005.1776)

- Part 2. Holographic metals.
- Reviews on the general aspects and motivation from CMT for strange metals:
- Sachdev's review http://arxiv.org/abs/1108.1197)

- Hartnoll's review http://arxiv.org/abs/arXiv:1106.4324

- Liu et al's review http://arxiv.org/abs/arXiv:1110.3814

- Polchinski http://arxiv.org/abs/hep-th/9210046

- Shankar http://arxiv.org/abs/cond-mat/9307009

- Sachdev's review http://arxiv.org/abs/1108.1197)
- Works which will be discussed:
- AdS RN black hole http://arxiv.org/abs/0903.2477

- semiholographic approach http://arxiv.org/abs/0912.1061, http://arxiv.org/abs/1001.5049

- electron star http://arxiv.org/abs/1008.2828

- Sachdev's model http://arxiv.org/abs/1107.5321

- dilatonic systems in CMT: e.g. Hartnoll http://arxiv.org/abs/arXiv:1111.2606, Sachdev
- http://arxiv.org/abs/1112.0573

- Lattice approach: e.g. http://arxiv.org/abs/1208.4102

- AdS RN black hole http://arxiv.org/abs/0903.2477

- Reviews on the general aspects and motivation from CMT for strange metals:

11.00 - 11.30 Coffee Break

11.30 - 12.30 Discussion session

12.30 - 16.30 Lunch

16.30 - 17.30

**Andrea Campoleoni** (Université Libre de Bruxelles, Belgium)

*Higher spins and dualities in various dimensions*

17.30 - 18.00 Coffee Break

18.00 - 19.00

**Andrea Campoleoni **(Université Libre de Bruxelles, Belgium)

*Higher spins and dualities in various dimensions
*

### Abstract and references

**Abstract
**We review the main features of the dualities between higher-spin gauge theories in 3 and 4 dimensions and conformal field theories. In both cases the bulk theory involves fields of spin greater than two coupled to matter according to a set of field equations proposed by Vasiliev. In three dimensions the conjectured boundary duals are W_N minimal models with extended conformal symmetry, while in four dimensions the dual is provided by the O(N) vector model in the large N limit. The main emphasis will be on the matching of symmetries on the two sides of the correspondence and on the role of the dimension of space-time, but a brief introduction to higher-spin theories will be also provided.

- M. A. Vasiliev, ``Higher spin gauge theories: Star product and AdS space,''

In *Shifman, M.A. (ed.): The many faces of the superworld* 533-610 [hep-th/9910096]. - M. R. Gaberdiel and R. Gopakumar, ``Minimal Model Holography,''

arXiv:1207.6697 [hep-th]. - S. Giombi and X. Yin, ``The Higher Spin/Vector Model Duality,''

arXiv:1208.4036 [hep-th].

19.00 - 20.00 Discussion session

## Thursday, December 20 - Aula Bianchi

9.00 - 11,00

**Francesco Benini** (Stony Brook University, USA)

**Stefano Cremonesi** (Imperial College, UK)

**Guido Festuccia** (Institute for Advanced Studies, USA)

**Sara Pasquetti** (University of Surrey, UK)

**Filippo Passerini** (CERN, Switzerland)

* Exact results in supersymmetric gauge theory on compact manifolds - part 1
*

### Abstract and references

**Abstract**

In recent years, supersymmetric localization has been applied to non-topological supersymmetric theories defined on compact manifolds. This method is extremely powerful, since it allows to compute exactly partition functions and the VEV of certain BPS operators, providing results for the non-perturbative dynamics of quantum fields. In this lecture, we will review how gauge theories can be defined on compact manifolds and explain the basic principles of supersymmetric localization.

- Rigid Supersymmetric Theories in Curved Superspace.

Guido Festuccia, Nathan Seiberg

JHEP 1106 (2011) 114

e-Print: arXiv:1105.0689 [hep-th] - Topological Quantum Field Theory.

Edward Witten

Commun.Math.Phys. 117 (1988) 353 - Localization of gauge theory on a four-sphere and supersymmetric Wilson loops.

Vasily Pestun

Commun.Math.Phys. 313 (2012) 71-129

e-Print: arXiv:0712.2824 [hep-th] - Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories.

Marcos Marino

J.Phys. A44 (2011) 463001

e-Print: arXiv:1104.0783 [hep-th]

11.00 - 11.30 Coffee Break

11.30 - 12.30 Discussion session

12.30 - 15.00 Lunch

15.00 - 17,00

**Francesco Benini** (Stony Brook University, USA)

**Stefano Cremonesi **(Imperial College, UK)

**Guido Festuccia** (Institute for Advanced Studies, USA)

**Sara Pasquetti** (University of Surrey, UK)

**Filippo Passerini **(CERN, Switzerland)

* Exact results in supersymmetric gauge theory on compact manifolds - part 2
*

### Abstract and references

**Abstract**

In this lecture we will review several applications of the localization techniques including non-perturbative dualities, line operators, holomorphic factorization of partition functions and application to non-linear sigma models.

- Exact Results for 't Hooft Loops in Gauge Theories on S^4.

Jaume Gomis, Takuya Okuda, Vasily Pestun

JHEP 1205 (2012) 141

e-Print: arXiv:1105.2568 [hep-th] - Wilson Loops in N=2 Super-Yang-Mills from Matrix Model.

F. Passerini and K. Zarembo

JHEP 1109 (2011) 102

e-Print: arXiv:1106.5763 [hep-th] - Exact results for vortex loop operators in 3d supersymmetric theories.

Nadav Drukker, Takuya Okuda, Filippo Passerini

e-Print: arXiv:1211.3409 [hep-th] - Exact results for supersymmetric abelian vortex loops in 2+1 dimensions.

Anton Kapustin, Brian Willett, Itamar Yaakov.

e-Print: arXiv:1211.2861 [hep-th] - Holomorphic Blocks in Three Dimensions.

Christopher Beem, Tudor Dimofte, Sara Pasquetti

e-Print: arXiv:1211.1986 [hep-th] - Factorisation of N = 2 Theories on the Squashed 3-Sphere.

Sara Pasquetti

JHEP 1204 (2012) 120

e-Print: arXiv:1111.6905 [hep-th] - Partition functions of N=(2,2) gauge theories on S^2 and vortices.

Francesco Benini, Stefano Cremonesi

e-Print: arXiv:1206.2356 [hep-th] - Exact Results in D=2 Supersymmetric Gauge Theories.

Nima Doroud, Jaume Gomis, Bruno Le Floch, Sungjay Lee

e-Print: arXiv:1206.2606 [hep-th]

17.00 - 17.30 Coffee Break

17.30 - 18.30 Discussion session

20.00 Social Dinner

## Friday, December 21 - Aula Bianchi

9.00 - 11,00

**Pierpaolo Mastrolia **(MPI-München, Germany and U. Padova and INFN, Italy)

**Giovanni Ossola **(City University of New York, USA)

* A new perspective on scattering amplitudes*

### Abstract and references

**Abstract**

Analyticity and Unitarity are generic mathematical properties which can be exploited for the determination of scattering amplitudes in gauge theories, achieved by processing the information contained in their multi-particle factorization channels. The multi-particle pole decomposition for the integrands of arbitrary scattering amplitudes emerges from the combination of analyticity and unitarity with the idea of a reduction under the integral sign. The principle of an integrand-reduction method is the existence of an integrand-reduction formula, namely a relation where the numerator of each Feynman integral is expressed as a combination of products of the corresponding denominators, with polynomial coefficients. The integrand-level methods for the reduction of scattering amplitudes

have already proven their effectiveness in several applications at one-loop, interesting for collider phenomenology. In this presentation we describe a new mathematical method to derive the integrand reduction formula for arbitrary amplitudes, regardless of the number of loop and of the particle content. This method is based on multivariate polynomial division, a technique that is used for the determination of the residue at any multi-particle cut, whose knowledge is a mandatory prerequisite for applying the integrand-reduction procedure. This technique yields the complete decomposition of arbitrary amplitudes in terms of independent integrals, that have to be finally evaluated in a successive step. We show its application to reduction of the two-loop five-point planar and non-planar scattering amplitudes in N = 4 SYM and N = 8 SUGRA.

- G. Ossola, C.G. Papadopoulos and R. Pittau,

``Reducing full one-loop amplitudes to scalar integrals at the

integrand level,''

Nucl. Phys. B763 (2007) 147 [hep-ph/0609007]. - R.K. Ellis, Z. Kunszt, K. Melnikov and G. Zanderighi,

``One-loop calculations in quantum field theory: from Feynman

diagrams to unitarity cuts,''

Phys. Rept. 518 (2012) 141 [arXiv:1105.4319 [hep-ph]]. - P. Mastrolia and G. Ossola,

``On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes,''

JHEP 1111 (2011) 014 [arXiv:1107.6041 [hep-ph]]. - P. Mastrolia, E. Mirabella, G. Ossola and T. Peraro,

``Integrand-Reduction for Two-Loop Scattering Amplitudes through

Multivariate Polynomial Division,''

Phys. Lett. B718 (2012) 173 [arXiv:1209.4319 [hep-ph]].

11.00 - 11.30 Coffee Break

11.30 - 12.30 Discussion session

12.30 Closing remarks