The second session today features physics closely associated with high energies.

Title comes from German phrase: Vielfalt statt Einfalt. Apparently hard to translate. Google suggests "variety is the spice of life" or "welcome as your are" or "be broad-minded, not narrow-minded".

Axions introduced for many reasons: strong CP problem, inflation, quintessence. From a string theory perspective, actually

Inflation needs nearly-flat potential for slow roll. Axion potential exactly perturbatively flat due to shift symmetry. Only non-perturbative instantons break this (to sinusoidal form).

Discussion about Planck and BICEP data. Of course, we now know BICEP claims about gravity waves were incorrect. Motivated work on two-axion fields were one rotates in potential of the other; this allows both to have axion scales

Two-axion potential has two contributions from instanton effects. Potential is "aligned" if one linear combination vanishes; leads to massless state. Natural to define an alignment parameter. Desired phenomenology comes in the nearly-aligned limit. Still, need to operate on the edge of perturbative control which demands a UV completion. SUSY is a reliable symmetry that can protect the axion potential.

The arguments done so far require that during inflation the axion is a small contribution to the superpotential. This implies that axionic inflation demands high-scale SUSY. However, only a small amount of model building leads to situations where SUSY is restored at the end of inflation. Some problem in trapping the saxion; simplest models allow saxion tunnelling and run away. But this can be solved with multiple axions.

Still have to address the Planck-scale question. Very flat potentials are susceptible to small deviations. Further, in single axion case have bound

Each slide in this talk is more technical than the last. We've somehow found ourselves talking about the weak gravity conjecture and black hole firewalls! But the talk is well-structured, while I'm not entirely on top of things I'm not exactly lost either.

String theory does not give sinusoidal potentials: it gives something more complex and wiggly. This is problematic for axion inflation. However, these subleading terms seem to help fix the trans-Planckian case somehow. But explicit calculations to fully resolve things not done?

A brief sideline to discuss similar idea in QCD axion models to solve domain wall problem.

Inflation is a remarkably successful

The tensor-to-scalar ratio

Chaotic inflation is simple model, and technically natural even for super-Planckian motion. Problem comes if inflaton is coupled to UV degrees of freedom of quantum gravity. Leads to infinite corrections to potential so that shape of potential can radically change. This also means that string theorists must meet a higher standard in justifying an inflationary potential than an effective field phenomenologist.

Back to axions. Multiple-axion fields, much like the previous talk. 20-30 different candidate models by now.

Also refer to axion monodromy. Not a true axion, as it has a perturbative mass. Modern theories less baroque than initial ideas. Use string torsion? Discrete translational symmetry persists in tricky way, leads to higher-order corrections being of the form of powers of the potential, protecting the corrections.

Multi-axion models, back to the aligned case. All techniques to get effective super-Planckian parameters.

Key question: is there a fundamental reason why single axion models have decay constants bounded from above? If so, can we avoid it with multi-axion theories or etc?

Back to the weak gravity conjecture. A nice explanation of what it is that either was missing or I missed in the previous talk. Specifically, conjectured that gravity is the weakest force: for every long-range gauge force, there exists a particle with charge greater than its mass. If voilated, then gravity will overcome gauge repulsion. Particles of same charge form stable bound states. Infinitely many of them, in fact. In particular, infinitely many stable BH states which

Strong form of conjecture demands the inequality be satisfied by the lightest charged state. The weak form simply demands that it be satisfied by

Conjecture relevant to axions because can be generalised to

Generalisation to multiple axion theories. Convex hull that was mentioned in previous talk.

**11:00 am:***Axions: Diversity beats Simplicity*, Hans Peter NillesTitle comes from German phrase: Vielfalt statt Einfalt. Apparently hard to translate. Google suggests "variety is the spice of life" or "welcome as your are" or "be broad-minded, not narrow-minded".

Axions introduced for many reasons: strong CP problem, inflation, quintessence. From a string theory perspective, actually

*too many*axions. So no problem in multiple axions, and point here is that can be a good thing. Connect to inflation, Planck data, alignment and SUSY.Inflation needs nearly-flat potential for slow roll. Axion potential exactly perturbatively flat due to shift symmetry. Only non-perturbative instantons break this (to sinusoidal form).

Discussion about Planck and BICEP data. Of course, we now know BICEP claims about gravity waves were incorrect. Motivated work on two-axion fields were one rotates in potential of the other; this allows both to have axion scales

*f*less than the Planck scale, but lead to*effective*trans-Planckian motion of the axion fields. See also "axion monodromy".Two-axion potential has two contributions from instanton effects. Potential is "aligned" if one linear combination vanishes; leads to massless state. Natural to define an alignment parameter. Desired phenomenology comes in the nearly-aligned limit. Still, need to operate on the edge of perturbative control which demands a UV completion. SUSY is a reliable symmetry that can protect the axion potential.

The arguments done so far require that during inflation the axion is a small contribution to the superpotential. This implies that axionic inflation demands high-scale SUSY. However, only a small amount of model building leads to situations where SUSY is restored at the end of inflation. Some problem in trapping the saxion; simplest models allow saxion tunnelling and run away. But this can be solved with multiple axions.

Still have to address the Planck-scale question. Very flat potentials are susceptible to small deviations. Further, in single axion case have bound

*f*less than string scale. Can a similar constrain be derived in multi-axion models?Each slide in this talk is more technical than the last. We've somehow found ourselves talking about the weak gravity conjecture and black hole firewalls! But the talk is well-structured, while I'm not entirely on top of things I'm not exactly lost either.

String theory does not give sinusoidal potentials: it gives something more complex and wiggly. This is problematic for axion inflation. However, these subleading terms seem to help fix the trans-Planckian case somehow. But explicit calculations to fully resolve things not done?

A brief sideline to discuss similar idea in QCD axion models to solve domain wall problem.

**11:45 am:***Inflation in String Theory*, Gary ShiuInflation is a remarkably successful

*effective*theory. Unfortunately, it is also bringing a whole slew of fine-tuning problems. Essentially, the slow roll conditions are very sensitive to Planck-scale corrections. Generically, higher-dimensional operators will spoil inflation. This makes string theory potentially useful; or alternatively, inflation offers one of the few experimental probes of strings.The tensor-to-scalar ratio

*r*is an important parameter for distinguishing different candidate models. As already noted,*r*bigger than 0.01 already implies trans-Planckian field evolution.Chaotic inflation is simple model, and technically natural even for super-Planckian motion. Problem comes if inflaton is coupled to UV degrees of freedom of quantum gravity. Leads to infinite corrections to potential so that shape of potential can radically change. This also means that string theorists must meet a higher standard in justifying an inflationary potential than an effective field phenomenologist.

Back to axions. Multiple-axion fields, much like the previous talk. 20-30 different candidate models by now.

Also refer to axion monodromy. Not a true axion, as it has a perturbative mass. Modern theories less baroque than initial ideas. Use string torsion? Discrete translational symmetry persists in tricky way, leads to higher-order corrections being of the form of powers of the potential, protecting the corrections.

Multi-axion models, back to the aligned case. All techniques to get effective super-Planckian parameters.

Key question: is there a fundamental reason why single axion models have decay constants bounded from above? If so, can we avoid it with multi-axion theories or etc?

Back to the weak gravity conjecture. A nice explanation of what it is that either was missing or I missed in the previous talk. Specifically, conjectured that gravity is the weakest force: for every long-range gauge force, there exists a particle with charge greater than its mass. If voilated, then gravity will overcome gauge repulsion. Particles of same charge form stable bound states. Infinitely many of them, in fact. In particular, infinitely many stable BH states which

*could*be problematic for ... reasons I missed.Strong form of conjecture demands the inequality be satisfied by the lightest charged state. The weak form simply demands that it be satisfied by

*a*charged state. Some hints from string Casimir that strong form holds if conjecture holds.Conjecture relevant to axions because can be generalised to

*p*-forms,*i.e.*axions. Except instantons are a qualitative difference so argument does not exactly follow. Try to exploit string T-duality. Conclude that for a large class of string axions, must be a instanton with a particular mass bound.Generalisation to multiple axion theories. Convex hull that was mentioned in previous talk.

__Questions__Challenge on whether the WGC is at all trustworthy. And thus whether the conclusions presented here are meaningful. Unfortunately, I'm not really able to properly judge the nature of this argument.
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