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## Main Question or Discussion Point

http://arxiv.org/abs/1808.03483

Sergio Cecotti, Cumrun Vafa

(Submitted on 10 Aug 2018)

In the context of N=2 supergravity without vector multiplets coupled to hypermultiplets, the coupling constant of graviphoton τ is apriori a free parameter. Stringy realization of this and using a mathematical conjecture leads to the statement that j(τ)∈R so that the θ-angle is 0 or π. We conjecture that for any consistent realization of N=2 supergravity theories coupled only to hypermultiplets this is the case and the rest belong to the swampland. This leads to the speculation that the θ-angle for QCD or QED may also be fixed to 0 for quantum gravitational consistency.

http://arxiv.org/abs/1808.04583

Matt Visser (Victoria University of Wellington)

(Submitted on 14 Aug 2018)

Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules:

$$\sum_n (−1)^{2S_n} g_n=0; \sum_n (−1)^{2S_n} g_n m_n^2 = 0; \sum_n (−1)^{2S_n} g_n m_n^4 = 0.$$ These three sum rules are intimately related to both the Lorentz invariance and the finiteness of the zero-point stress-energy tensor. Further afield, these three constraints are also intimately related to the existence of finite QFTs ultimately based on fermi--bose cancellations. (Supersymmetry is neither necessary nor sufficient for the existence of these finite QFTs; though softly but explicitly broken supersymmetry can be used as a book-keeping device to keep the calculations manageable.) In the current article I shall instead take these three Pauli sum rules as given, assume their exact non-perturbative validity, contrast them with the observed standard model particle physics spectrum, and use them to extract as much model-independent information as possible regarding beyond standard model (BSM) physics.

**Theta-problem and the String Swampland**Sergio Cecotti, Cumrun Vafa

(Submitted on 10 Aug 2018)

In the context of N=2 supergravity without vector multiplets coupled to hypermultiplets, the coupling constant of graviphoton τ is apriori a free parameter. Stringy realization of this and using a mathematical conjecture leads to the statement that j(τ)∈R so that the θ-angle is 0 or π. We conjecture that for any consistent realization of N=2 supergravity theories coupled only to hypermultiplets this is the case and the rest belong to the swampland. This leads to the speculation that the θ-angle for QCD or QED may also be fixed to 0 for quantum gravitational consistency.

http://arxiv.org/abs/1808.04583

**The Pauli sum rules imply BSM physics**Matt Visser (Victoria University of Wellington)

(Submitted on 14 Aug 2018)

Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules:

$$\sum_n (−1)^{2S_n} g_n=0; \sum_n (−1)^{2S_n} g_n m_n^2 = 0; \sum_n (−1)^{2S_n} g_n m_n^4 = 0.$$ These three sum rules are intimately related to both the Lorentz invariance and the finiteness of the zero-point stress-energy tensor. Further afield, these three constraints are also intimately related to the existence of finite QFTs ultimately based on fermi--bose cancellations. (Supersymmetry is neither necessary nor sufficient for the existence of these finite QFTs; though softly but explicitly broken supersymmetry can be used as a book-keeping device to keep the calculations manageable.) In the current article I shall instead take these three Pauli sum rules as given, assume their exact non-perturbative validity, contrast them with the observed standard model particle physics spectrum, and use them to extract as much model-independent information as possible regarding beyond standard model (BSM) physics.