8 research outputs found
The AdS/CFT Correspondence and Symmetry Breaking
In the first part of this thesis we study baryonic U(1) symmetries dual to
Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau
4-fold singularities. We begin by focusing on isolated toric singularities
without vanishing 6-cycles, which we classify, and propose for them field
theory duals. We then study in detail the cone over Q^111 and find agreement
between the spectrum of baryonic operators in this theory and M5 branes
wrapping 5-cycles in the Q^111 space. The physics of vacua in which these
symmetries are spontaneously broken precisely matches a dual gravity analysis
involving resolutions of the singularity, where we are able to match
condensates, Goldstone bosons and global strings. We then study the
implications of turning on a torsion 4-form flux. This flux non-trivially
affects the supergravity dual of Higgsing, and we show that the supergravity
and field theory analyses precisely match in an example based on Y^12(CP^2). We
then explain how the choice of M-theory circle can result in exotic
renormalization group flows. We also argue that theories where the resolutions
have 6-cycles are expected to receive non-perturbative corrections from M5
instantons. We give a general formula relating the instanton action to
normalizable harmonic 2-forms.
In the second part of this thesis we study the breaking of baryonic
symmetries in the AdS_5/CFT_4 correspondence. This leads, for particular vacuum
expectation values, to the emergence of baryonic symmetries during the
renormalization group flow. We identify these vacuum expectation values with
critical values of the B-field moduli in the dual supergravity backgrounds. We
study in detail the C^3/Z_3 orbifold theory and the dual supergravity
backgrounds that correspond to the breaking of the emerging baryonic
symmetries, and identify the expected Goldstone bosons and global strings in
the IR.Comment: PhD thesis, University of Oxford, September 201
(Un)Higgsing the M2-brane
We study various aspects of N=2 quiver-Chern-Simons theories, conjectured to
be dual to M2-branes at toric Calabi-Yau four-fold singularities, under
Higgsing. In particular we study in detail the orbifold C^4/Z_2^3, obtaining a
number of different quiver-Chern-Simons phases for this model, and all 18 toric
partial resolutions thereof. In the process we develop a general un-Higgsing
algorithm that allows one to construct quiver-Chern-Simons theories by blowing
up, thus obtaining a plethora of new models. In addition we explain how turning
on torsion G-flux non-trivially affects the supergravity dual of Higgsing,
showing that the supergravity and field theory analyses precisely match in an
example based on the Sasaki-Einstein manifold Y^(1,2)(CP^2).Comment: 68 pages, a plethora of figures; v2: minor changes, published versio
Emerging Non-Anomalous Baryonic Symmetries in the AdS_5/CFT_4 Correspondence
We study the breaking of baryonic symmetries in the AdS_5/CFT_4
correspondence for D3 branes at Calabi-Yau three-fold singularities. This
leads, for particular VEVs, to the emergence of non-anomalous baryonic
symmetries during the renormalization group flow. We claim that these VEVs
correspond to critical values of the B-field moduli in the dual supergravity
backgrounds. We study in detail the C^3/Z_3 orbifold, the cone over F_0 and the
C^3/Z_5 orbifold. For the first two examples, we study the dual supergravity
backgrounds that correspond to the breaking of the emerging baryonic symmetries
and identify the expected Goldstone bosons and global strings in the infra-red.
In doing so we confirm the claim that the emerging symmetries are indeed
non-anomalous baryonic symmetries.Comment: 65 pages, 15 figures;v2: minor changes, published versio
Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence
We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3
correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of
the boundary conditions for vector fields in AdS_4 allows for a choice where
wrapped M5 brane states carrying non-zero charge under such symmetries can be
considered. We begin by focusing on isolated toric singularities without
vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary
conditions considered are dual to a CFT where the gauge group is U(1)^2 x
SU(N)^4. We find agreement between the spectrum of gauge-invariant
baryonic-type operators in this theory and wrapped M5 brane states. Moreover,
the physics of vacua in which these symmetries are spontaneously broken
precisely matches a dual gravity analysis involving resolutions of the
singularity, where we are able to match condensates of the baryonic operators,
Goldstone bosons and global strings. We also argue more generally that theories
where the resolutions have six-cycles are expected to receive non-perturbative
corrections from M5 brane instantons. We give a general formula relating the
instanton action to normalizable harmonic two-forms, and compute it explicitly
for the Q^{222} example. The holographic interpretation of such instantons is
currently unclear.Comment: 92 pages, 10 figure
The AdS/CFT correspondence and symmetry breaking
In the first part of this thesis we study baryonic U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Such short multiplets originate from the Kaluza-Klein compactification of eleven-dimensional supergravity on the corresponding Sasaki-Einstein seven-manifolds. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, which we classify, and propose for them field theory duals. We then study in detail the cone over the well-known Sasaki-Einstein space Q^111, which is a U(1) fibration over CP^1 x CP^1 x CP^1. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and M5 branes wrapping five-cycles in the Q^111 space. Moreover, the physics of vacua in
which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We then study the implications of turning on a closed three-form with non-zero periods through torsion three cycles in the Sasaki-Einstein manifold. This three-form, otherwise known as torsion G-flux, non-trivially affects the supergravity dual of Higgsing, and we show that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^1,2(CP^2), which is a S^3 bundle over CP^2. We then explain how the choice of M-theory circle in the background can result in exotic renormalization group flows in the dual field theory, and study this in detail for the Sasaki-Einstein manifold Y^1,2(CP^2). We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Sasaki-Einstein Q^222 example, which is a Z_2 orbifold of Q^111 in which the free Z_2 quotient is along the R-symmetry U(1) fibre. The holographic interpretation of such instantons is currently unclear.
In the second part of this thesis we study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at Calabi-Yau three-fold singularities. This leads, for particular vacuum expectation values, to the emergence of non-anomalous baryonic symmetries during the renormalization group flow. We identify these vacuum expectation values with critical values of the NS-NS B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold theory and the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries, and identify the expected Goldstone bosons and global strings in the
infra-red. In doing so we confirm the claim that the emerging symmetries are indeed non-anomalous baryonic symmetries