## Periodic Reporting for period 3 - SM-GRAV (Gravity, Holography and The Standard Model)

Reporting period: 2019-01-01 to 2020-06-30

"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,m, 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 the black hole information paradox,

epitomize such clash between quantum mechanics and gravity.

This clash indicates that we need to understand gravity further and its marriage to quantum mechanis in order to understand

the rules that govern our physical world.

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.

Instead of

relying on the string picture of the unification of all interactions with

gravity, the dual language of four-dimensional quantum field

theories is contrasted.

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 theoiries

(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)

The key idea is that gravity, as

observed in nature, is emergent: the graviton is not a fundamental field in the description.

It is rathere a composite of other fundamental degrees opf freedom, similar to those we have in our description of elementary

particle interactions.

There are, however, many questions that need to be

addressed in order for this setup to be a viable physical theory:

1. Why is the gravitational force four-dimensional (instead of higher-dimensional as

suggested by standard holography)?

2. Why does the coupling of the

gravitational force to the SM satisfy the equivalence principle (all masses fall the same way in a gravitational field) to such a high

accuracy?

3. What are other universal interactions with the SM model implied

in this picture? What are their phenomenological consequences?

4. How can one

construct, precise and controllable models for this setup?

5. How this setup adresses the cosmological constant problem?

6. How is cosmology emerging in this picture? How do the important problems associated

with it get resolved?

The present project, SM-GRAV, is addressing all of the above questions using the

tools of quantum field theory, of string theory and the holographic (AdS-CFT) correspondence.

"

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,m, 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 the black hole information paradox,

epitomize such clash between quantum mechanics and gravity.

This clash indicates that we need to understand gravity further and its marriage to quantum mechanis in order to understand

the rules that govern our physical world.

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.

Instead of

relying on the string picture of the unification of all interactions with

gravity, the dual language of four-dimensional quantum field

theories is contrasted.

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 theoiries

(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)

The key idea is that gravity, as

observed in nature, is emergent: the graviton is not a fundamental field in the description.

It is rathere a composite of other fundamental degrees opf freedom, similar to those we have in our description of elementary

particle interactions.

There are, however, many questions that need to be

addressed in order for this setup to be a viable physical theory:

1. Why is the gravitational force four-dimensional (instead of higher-dimensional as

suggested by standard holography)?

2. Why does the coupling of the

gravitational force to the SM satisfy the equivalence principle (all masses fall the same way in a gravitational field) to such a high

accuracy?

3. What are other universal interactions with the SM model implied

in this picture? What are their phenomenological consequences?

4. How can one

construct, precise and controllable models for this setup?

5. How this setup adresses the cosmological constant problem?

6. How is cosmology emerging in this picture? How do the important problems associated

with it get resolved?

The present project, SM-GRAV, is addressing all of the above questions using the

tools of quantum field theory, of string theory and the holographic (AdS-CFT) correspondence.

"

"

The research for the first 2.5 years on Advanced ERC project ""SM-GRAV"" was

focused in the following directions.

1) 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. Such flows track

the change of a quantum theory under a change of scale due to quantum effects.

There was a series of works in this direction that analyzed in full generality

the equations of the gravitational description and their translation in quantum

field theory language.

What was found was a wealth of cases which were not known before and whose

study was initiated.

These involved solutions that interpolate between two minima of the potential,

solutions that are patch-wise defined and cases where there is a dynamical

competition of solutions.

The analysis of such solutions went even further, by considering quantum field

theories that lived on curved space-time. There were many reasons to consider

this. Probably the most interesting is that we would like to understand the

response of quantum field theory being in de Sitter space. de Sitter space is a

highly symmetric space that is describing the cosmological expansion in an

accelerating phase of the universe, similar to the one our universe is

undergoing currently.

There are many puzzles concerning quantum field theories in de Sitter space

and some were addressed in the on-going work.

One of the most important outcomes of this work is to provide a controlled

calculation of the back-reaction of the quantum field theory on the geometry,

an effect that has been postulated in the back, but it physical impact has been

out of reach so far.

A further study, analyzed the black-hole solutions in this general landscape.

On one hand black-holes are the most iconic solutions/backrounds for gravity.

On the other, via the holographic correspondence they describe the finite

temperature physics of the dual quantum field theories.

2) The second direction involved use of the ideas mentioned above to readdress

the cosmological constant problem, one of the most serious clash points of

gravity versus quantum mechanics.

The problem can be described as follows:

a) A direct calculation in quantum field theories yields the energy (density)

of the vacuum to be very large (of order the Planck Mass to the fourth power)

b) The energy-density of the vacuum today is also inferred using the

gravitational theory and cosmological observations on the acceleration of the

expansion of the universe. This yields a value for the vacuum energy density

that is 120 orders of magnitude smaller compared to the one predicted by the

quantum field theory describing the fundamental particle interactions.

In our setup we can consider a gravitational form of the interaction of our

four-dimensional world of elementary particle interactions as a

four-dimensional mem(brane) stretching inside a five-dimensional space that is

generated by the gravitational description of the hidden quantum field theory

that generates gravity. This brane-world picture of our world is not new and

has been studied before.

What we have managed however is to implement the self-tuning idea on the

cosmological constant in this context as follows: The known interactions

generate a large vacuum energy (= cosmological constant) that is localized on

the four-dimensional universe brane. This large cosmological constant will

become ""invisible"" if the universe on the brane does not expand.

We therefore searched for solutions in the full theory such that the brane

metric is flat. To do this, we made a detailed analysis of the bulk equations

of motion and of the interaction of the brane and the bulk. 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. Moreover, the mass of the brane graviton is controlled by the number

of different particles of the hidden quantum field theory and can be made

arbitrarily small. We have also analyzed other scalar interactions that are

induced on the brane and gave conditions for their good behavior.

We have also found solutions where our brane world is curved and expanding.

There are several directions towards which our studies above lead and are

currently under study:

a) The cosmology associated with moving branes in the brane-world setup, which

is a necessary ingredient in any self-tuning resolution of the cosmological

constant problem.

This is technically notoriously difficult but we have made substantial progress

and we have mastered it in the probe brane approximation. This work is

on-going.

b) The study of the cosmology associated with induced gravity actions

calculated by integrating out quantum field theories.

c) The detailed study of realistic models of self-tuning.

d) The connection between the self-tuning of the cosmological constant and the

hierarchy problem by including the Higgs fields in the self-tuning process.

"

The research for the first 2.5 years on Advanced ERC project ""SM-GRAV"" was

focused in the following directions.

1) 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. Such flows track

the change of a quantum theory under a change of scale due to quantum effects.

There was a series of works in this direction that analyzed in full generality

the equations of the gravitational description and their translation in quantum

field theory language.

What was found was a wealth of cases which were not known before and whose

study was initiated.

These involved solutions that interpolate between two minima of the potential,

solutions that are patch-wise defined and cases where there is a dynamical

competition of solutions.

The analysis of such solutions went even further, by considering quantum field

theories that lived on curved space-time. There were many reasons to consider

this. Probably the most interesting is that we would like to understand the

response of quantum field theory being in de Sitter space. de Sitter space is a

highly symmetric space that is describing the cosmological expansion in an

accelerating phase of the universe, similar to the one our universe is

undergoing currently.

There are many puzzles concerning quantum field theories in de Sitter space

and some were addressed in the on-going work.

One of the most important outcomes of this work is to provide a controlled

calculation of the back-reaction of the quantum field theory on the geometry,

an effect that has been postulated in the back, but it physical impact has been

out of reach so far.

A further study, analyzed the black-hole solutions in this general landscape.

On one hand black-holes are the most iconic solutions/backrounds for gravity.

On the other, via the holographic correspondence they describe the finite

temperature physics of the dual quantum field theories.

2) The second direction involved use of the ideas mentioned above to readdress

the cosmological constant problem, one of the most serious clash points of

gravity versus quantum mechanics.

The problem can be described as follows:

a) A direct calculation in quantum field theories yields the energy (density)

of the vacuum to be very large (of order the Planck Mass to the fourth power)

b) The energy-density of the vacuum today is also inferred using the

gravitational theory and cosmological observations on the acceleration of the

expansion of the universe. This yields a value for the vacuum energy density

that is 120 orders of magnitude smaller compared to the one predicted by the

quantum field theory describing the fundamental particle interactions.

In our setup we can consider a gravitational form of the interaction of our

four-dimensional world of elementary particle interactions as a

four-dimensional mem(brane) stretching inside a five-dimensional space that is

generated by the gravitational description of the hidden quantum field theory

that generates gravity. This brane-world picture of our world is not new and

has been studied before.

What we have managed however is to implement the self-tuning idea on the

cosmological constant in this context as follows: The known interactions

generate a large vacuum energy (= cosmological constant) that is localized on

the four-dimensional universe brane. This large cosmological constant will

become ""invisible"" if the universe on the brane does not expand.

We therefore searched for solutions in the full theory such that the brane

metric is flat. To do this, we made a detailed analysis of the bulk equations

of motion and of the interaction of the brane and the bulk. 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. Moreover, the mass of the brane graviton is controlled by the number

of different particles of the hidden quantum field theory and can be made

arbitrarily small. We have also analyzed other scalar interactions that are

induced on the brane and gave conditions for their good behavior.

We have also found solutions where our brane world is curved and expanding.

There are several directions towards which our studies above lead and are

currently under study:

a) The cosmology associated with moving branes in the brane-world setup, which

is a necessary ingredient in any self-tuning resolution of the cosmological

constant problem.

This is technically notoriously difficult but we have made substantial progress

and we have mastered it in the probe brane approximation. This work is

on-going.

b) The study of the cosmology associated with induced gravity actions

calculated by integrating out quantum field theories.

c) The detailed study of realistic models of self-tuning.

d) The connection between the self-tuning of the cosmological constant and the

hierarchy problem by including the Higgs fields in the self-tuning process.

"

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

Further expected results

A. A general description of emergent gravity in QFT

B. A general description of emerging gauge theory in QFT

C. A general description of emerging axions in QFT

D. A connection between the self-tuning of the cosmological constant and the hierarchy problem

E. Phenomenological implications of emerged gravity, axions and dark photons.

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

Further expected results

A. A general description of emergent gravity in QFT

B. A general description of emerging gauge theory in QFT

C. A general description of emerging axions in QFT

D. A connection between the self-tuning of the cosmological constant and the hierarchy problem

E. Phenomenological implications of emerged gravity, axions and dark photons.