## Thesis etd-05252016-020254 |

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Thesis type

Tesi di laurea magistrale

Author

MANENTI, ANDREA

URN

etd-05252016-020254

Thesis title

Holographic computation of the Neutron Electric Dipole Moment

Department

FISICA

Course of study

FISICA

Supervisors

**relatore**Dott. Bigazzi, Francesco

Keywords

- AdS/CFT correspondence
- Chromodynamics
- dipole moment
- gauge gravity duality
- holography
- instantons
- QCD
- string theory
- topological term

Graduation session start date

21/07/2016

Availability

Full

Summary

The final aim of the thesis is the computation of the Neutron electric dipole moment in the theory of

Quantum Chromodynamics. This quantity is easily accessible experimentally and it is P and T violating,

so the physical interest consists in the possibility of investigating an eventual P, T violation in QCD.

The computation will be performed in the framework of AdS/CFT correspondence, in particular we

use the Sakai–Sugimoto model, in which some deformation are added in order to include masses to

quarks and a non zero theta parameter. The baryons in this model correspond to instantons in a Yang-Mills - Chern-Simons theory, in analogy with the Skyrme model where they correspond to Skyrmions.

Standard quantum mechanic techniques allow us to quantize these solution and to study their properties,

such as the electric dipole moment.

The work will be organized as follows: first of all we make an introduction to the AdS/CFT cor-

respondence, the basic tools of String theory, AdS geometry and D-branes are briefly summarized and

then combined to formulate the correspondence, along with a simple example. After this we discuss some

important non perturbative aspects of QCD, among them the topological properties,

instantons and large N expansion. Then we focus on the Witten's background for QCD, obtained

from a supersymmetry breaking compactification in Type II A Supergravity, this is interpreted as a dual

of Yang-Mills at low energies. Then the Sakai-Sugimoto model is introduced, which is a setting of

D8 branes in the Witten's background, this allows us to describe massless quarks. We then move to

the necessary deformations needed to pursue our final computation. Masses to quarks are introduced via

a non local term, they are necessary to have a non trivial theta dependence because the U(1)A anomaly

has naturally an holographic counterpart. The theta parameter is simply related to a background value of

the RR 1 form, which, when the masses are present, can be absorbed in the abelian gauge field. Then

follows a review of the instantonic solution of this model, its moduli space and the quantization. This

solution is the holographic dual of a baryon, we compute in addition the correction to the baryon mass

in presence of a theta parameter. The last part is the actual computation of the electric dipole moment of

the neutron, some previous results obtained with different methods are shown. First of all we solve the

Yang-Mills - Chern-Simons equations of motion on the D8 branes in presence of the mass perturbation,

then we quantize the solution via standard methods and extract the Neutron Electric Dipole moment, to

first order in the quark masses and in the theta parameter, in the case of two degenerate flavours. The idea

of the computation is inspired to the Skyrme model's counterpart.

Quantum Chromodynamics. This quantity is easily accessible experimentally and it is P and T violating,

so the physical interest consists in the possibility of investigating an eventual P, T violation in QCD.

The computation will be performed in the framework of AdS/CFT correspondence, in particular we

use the Sakai–Sugimoto model, in which some deformation are added in order to include masses to

quarks and a non zero theta parameter. The baryons in this model correspond to instantons in a Yang-Mills - Chern-Simons theory, in analogy with the Skyrme model where they correspond to Skyrmions.

Standard quantum mechanic techniques allow us to quantize these solution and to study their properties,

such as the electric dipole moment.

The work will be organized as follows: first of all we make an introduction to the AdS/CFT cor-

respondence, the basic tools of String theory, AdS geometry and D-branes are briefly summarized and

then combined to formulate the correspondence, along with a simple example. After this we discuss some

important non perturbative aspects of QCD, among them the topological properties,

instantons and large N expansion. Then we focus on the Witten's background for QCD, obtained

from a supersymmetry breaking compactification in Type II A Supergravity, this is interpreted as a dual

of Yang-Mills at low energies. Then the Sakai-Sugimoto model is introduced, which is a setting of

D8 branes in the Witten's background, this allows us to describe massless quarks. We then move to

the necessary deformations needed to pursue our final computation. Masses to quarks are introduced via

a non local term, they are necessary to have a non trivial theta dependence because the U(1)A anomaly

has naturally an holographic counterpart. The theta parameter is simply related to a background value of

the RR 1 form, which, when the masses are present, can be absorbed in the abelian gauge field. Then

follows a review of the instantonic solution of this model, its moduli space and the quantization. This

solution is the holographic dual of a baryon, we compute in addition the correction to the baryon mass

in presence of a theta parameter. The last part is the actual computation of the electric dipole moment of

the neutron, some previous results obtained with different methods are shown. First of all we solve the

Yang-Mills - Chern-Simons equations of motion on the D8 branes in presence of the mass perturbation,

then we quantize the solution via standard methods and extract the Neutron Electric Dipole moment, to

first order in the quark masses and in the theta parameter, in the case of two degenerate flavours. The idea

of the computation is inspired to the Skyrme model's counterpart.

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