Periodic Reporting for period 4 - SM-GRAV (Gravity, Holography and The Standard Model)
Periodo di rendicontazione: 2020-07-01 al 2021-09-30
The two pillars of modern physics is the theory of elementary particles and their interactions and the theory of gravity. The first relies on quantum mechanics and the special theory of relativity while the second on the general theory of relativity.
Both theories are extremely successfull in describing the physical world, and in some cases their accuracy is astonishing.
When however they involve phenomena where both quantum and gravitational aspects are present they give widely different results and puzzles. The cosmological constant problem and the black hole information paradox, epitomize such clash between quantum mechanics and gravity.
The main thrust of this project is to investigate implications of a recently
discovered correspondence (string theory/gravity vs. gauge theory) to the
physics of the fundamental interactions and its coupling to gravity.
Such a different perspective is expected to provide three distinct results:
(a) A view of the theory of the particle interactions and its embedding in string theory that is describable by quantum field theories
(b) Novel phenomena and properties of such embeddings that are hard to see in the string theory picture.
(c) A "dual" view that would be valid in non-stringy regimes (which may be well described by QFT)
Both theories are extremely successfull in describing the physical world, and in some cases their accuracy is astonishing.
When however they involve phenomena where both quantum and gravitational aspects are present they give widely different results and puzzles. The cosmological constant problem and the black hole information paradox, epitomize such clash between quantum mechanics and gravity.
The main thrust of this project is to investigate implications of a recently
discovered correspondence (string theory/gravity vs. gauge theory) to the
physics of the fundamental interactions and its coupling to gravity.
Such a different perspective is expected to provide three distinct results:
(a) A view of the theory of the particle interactions and its embedding in string theory that is describable by quantum field theories
(b) Novel phenomena and properties of such embeddings that are hard to see in the string theory picture.
(c) A "dual" view that would be valid in non-stringy regimes (which may be well described by QFT)
OVERVIEW OF THE RESEARCH PERFORMED IN SM-GRAV
The research for the Advanced ERC project "SM-GRAV" has focused in the following four directions, that comprise the basic tasks of the project.
Task 1) This task involved the investigation of the gravitational landscape of theories and the navigation of this landscape via classical solutions that are holographically dual to renormalization group flows in quantum field theory. What was found was a wealth of cases which were not known before and whose study was initiated.
These involved novel types of solutions that:
(a) interpolate between two minima of the potential (a set that will become crucial in a subsequent study of the Coleman-de Luccia gravitational instabilities),
(b) solutions that are patch-wise defined due to the fact that the direction of the flow inverts without the flow stopping. We have called such a phenomenon a “bounce”
(c) Multiple solutions from a single UV fixed point where there is a dynamical competition. In such cases, at least one of the competing solutions skips the next fixed point. We have called such solutions, “skipping flows”.
The analysis of holographic RG flows went even further, by considering quantum field theories that lived on curved space-times. We have analyzed RG flows of holographic QFTs on manifolds that are products of spheres and hyperbolic spaces. The exotic flows persist and generalize in the presence of curvature. New phenomena were found, like the spontaneous breaking of spacetime symmetries, seen in the simplest example of holographic CFTs on S2x S2.
Another application of our results on de Sitter and anti de Sitter flows were eventually applied to a very interesting problem, that of self-tuning branes that will be described in more detail in task 4.
It was realized that minimum to minimum flows in the Euclidean regime are precisely Coleman-de Luccia (CdL) instantons driving a bubble instability of the unstable potential minimum associated with the UV CFT. What we have shown is that such solutions do not exist for generic potentials, and that they exist only if the scalar potential admits flat skipping flows.
We have given also an algorithm on how to construct scalar potentials so that such instantons exist.
Task 2) This task was dominated by the study of emergent gravity along the lines set by the AdS-CFT correspondence.
We have investigated in detail emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor in any QFT.
We have derived the general effective description of such dynamics using the concept of the effective action of the emergent graviton. A study in a single QFT, indicates that in the linearized regime, generically, such gravity is massive if the theory is gapped. In massless theories on the other hand a continuum of gravitons appears, stretching down to zero mass. The tensor combination of the linearized emergent gravitational force is that associated with massive graviton exchange.
An important property of emergent gravity from a QFT defined on a Minkowski metric is that it always has the Minkowski metric as a solution, independent of quantum corrections. To this, the fact that the theory is a bigravity theory plays an important role. This remarkable property is a first non-trivial step towards a resolution of the cosmological constant problem.
Task 3) In this task various avatars of the emergent gravity idea were studied.
The first was the fact that generically, a universal axion appears at the same time as the emergent graviton. A special property of holographic emergent axions, that set them apart from other types, is that the interaction they mediate, is four-dimensional at large and short distances but may be five dimensional at intermediate distances.
An important problem solved was to understand the bulk physics of such axions, as it has many implications for different types of contexts.
Another set of emergent light fields that we studied are vectors, that arise from conserved currents in the hidden theory. Such vectors are avatars of emergent gravity and for this reason we call them “graviphotons”. They have similarities to string theory graviphotons. They may have important and/or dangerous couplings to the Standard model.
As SM fields are generically chargeless under such graviphotons, the most dangerous coupling is the mixing with a hypercharge.
Task 4)
In this task several important problems for emergent gravity were studied in the gravitational formulation, namely a bulk five-dimensional theory dual to the hidden holographic QFT together with a SM brane embedded in the bulk, and interacting with the bulk fields.
What we have managed, is to implement the self-tuning idea on the cosmological constant in this context as follows: we searched for solutions in the full theory such that the brane metric is flat despite a brane cosmological constant. We found that generically
A. such solutions exist
B. they are free of bad singularities.
We have further analyzed the nature of the gravitational interaction on the universe brane, and found that quite generally gravity was four-dimensional and massive
.
Finally, we have studied the possibility of connecting the self-tuning of the cosmological constant with the hierarchy problem of the Standard Model associated to the Higgs mass.
We have found that the bulk universal axion, generates a multitude of solutions that can be used to solve the hierarchy problem.
The research for the Advanced ERC project "SM-GRAV" has focused in the following four directions, that comprise the basic tasks of the project.
Task 1) This task involved the investigation of the gravitational landscape of theories and the navigation of this landscape via classical solutions that are holographically dual to renormalization group flows in quantum field theory. What was found was a wealth of cases which were not known before and whose study was initiated.
These involved novel types of solutions that:
(a) interpolate between two minima of the potential (a set that will become crucial in a subsequent study of the Coleman-de Luccia gravitational instabilities),
(b) solutions that are patch-wise defined due to the fact that the direction of the flow inverts without the flow stopping. We have called such a phenomenon a “bounce”
(c) Multiple solutions from a single UV fixed point where there is a dynamical competition. In such cases, at least one of the competing solutions skips the next fixed point. We have called such solutions, “skipping flows”.
The analysis of holographic RG flows went even further, by considering quantum field theories that lived on curved space-times. We have analyzed RG flows of holographic QFTs on manifolds that are products of spheres and hyperbolic spaces. The exotic flows persist and generalize in the presence of curvature. New phenomena were found, like the spontaneous breaking of spacetime symmetries, seen in the simplest example of holographic CFTs on S2x S2.
Another application of our results on de Sitter and anti de Sitter flows were eventually applied to a very interesting problem, that of self-tuning branes that will be described in more detail in task 4.
It was realized that minimum to minimum flows in the Euclidean regime are precisely Coleman-de Luccia (CdL) instantons driving a bubble instability of the unstable potential minimum associated with the UV CFT. What we have shown is that such solutions do not exist for generic potentials, and that they exist only if the scalar potential admits flat skipping flows.
We have given also an algorithm on how to construct scalar potentials so that such instantons exist.
Task 2) This task was dominated by the study of emergent gravity along the lines set by the AdS-CFT correspondence.
We have investigated in detail emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor in any QFT.
We have derived the general effective description of such dynamics using the concept of the effective action of the emergent graviton. A study in a single QFT, indicates that in the linearized regime, generically, such gravity is massive if the theory is gapped. In massless theories on the other hand a continuum of gravitons appears, stretching down to zero mass. The tensor combination of the linearized emergent gravitational force is that associated with massive graviton exchange.
An important property of emergent gravity from a QFT defined on a Minkowski metric is that it always has the Minkowski metric as a solution, independent of quantum corrections. To this, the fact that the theory is a bigravity theory plays an important role. This remarkable property is a first non-trivial step towards a resolution of the cosmological constant problem.
Task 3) In this task various avatars of the emergent gravity idea were studied.
The first was the fact that generically, a universal axion appears at the same time as the emergent graviton. A special property of holographic emergent axions, that set them apart from other types, is that the interaction they mediate, is four-dimensional at large and short distances but may be five dimensional at intermediate distances.
An important problem solved was to understand the bulk physics of such axions, as it has many implications for different types of contexts.
Another set of emergent light fields that we studied are vectors, that arise from conserved currents in the hidden theory. Such vectors are avatars of emergent gravity and for this reason we call them “graviphotons”. They have similarities to string theory graviphotons. They may have important and/or dangerous couplings to the Standard model.
As SM fields are generically chargeless under such graviphotons, the most dangerous coupling is the mixing with a hypercharge.
Task 4)
In this task several important problems for emergent gravity were studied in the gravitational formulation, namely a bulk five-dimensional theory dual to the hidden holographic QFT together with a SM brane embedded in the bulk, and interacting with the bulk fields.
What we have managed, is to implement the self-tuning idea on the cosmological constant in this context as follows: we searched for solutions in the full theory such that the brane metric is flat despite a brane cosmological constant. We found that generically
A. such solutions exist
B. they are free of bad singularities.
We have further analyzed the nature of the gravitational interaction on the universe brane, and found that quite generally gravity was four-dimensional and massive
.
Finally, we have studied the possibility of connecting the self-tuning of the cosmological constant with the hierarchy problem of the Standard Model associated to the Higgs mass.
We have found that the bulk universal axion, generates a multitude of solutions that can be used to solve the hierarchy problem.
1. A deep study of holographic RG flows beyond the state of the art and their impact in the mapping of the gravitational landscape.
2. A working mechanism for the holographic self-tuning of the cosmological constant
3. A new approach to F-functions in quantum field theory
4. A cosmological setup for the self-tuning mechanism and connection with the hierarchy problem
5. The mechanism for emergent gravity and its implications for the cosmological constant problem.
6. A general description of emerging gauge theory in QFT
7. A general description of emerging axions in QFT
2. A working mechanism for the holographic self-tuning of the cosmological constant
3. A new approach to F-functions in quantum field theory
4. A cosmological setup for the self-tuning mechanism and connection with the hierarchy problem
5. The mechanism for emergent gravity and its implications for the cosmological constant problem.
6. A general description of emerging gauge theory in QFT
7. A general description of emerging axions in QFT