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Princeton University

1. Fei, Lin. Conformal Field Theories in the Epsilon and 1/N Expansions .

Degree: PhD, 2017, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp0144558g94m

In this thesis, we study various conformal field theories in two different approximation schemes - the epsilon-expansion in dimensional continuation, and the large N expansion. We first propose a cubic theory in d=6-epsilon as the UV completion of the quartic scalar O(N) theory in d>4. We study this theory to three-loop order and show that various operator dimensions are consistent with large-N results. This theory possesses an IR stable fixed point at real couplings for N>1038, suggesting the existence of a perturbatively unitary interacting O(N) symmetric CFT in d=5. Extending this model to Sp(N) symmetric theories, we find an interacting non-unitary CFT in d=5. For the special case of Sp(2), the IR fixed point possesses an enhanced symmetry given by the supergroup OSp(1|2). We also observe that various operator dimensions of the Sp(2) theory match those from the 0-state Potts model. We provide a graph theoretic proof showing that the zero, two, and three-point functions in the Sp(2) model and the 0-state Potts model indeed match to all orders in perturbation theory, strongly suggesting their equivalence. We then study two fermionic theories in d=2+epsilon - the Gross-Neveu model and the Nambu-Jona-Lasinio model, together with their UV completions in d=4-epsilon given by the Gross-Neveu-Yukawa and the Nambu-Jona-Lasinio-Yukawa theories. We compute their sphere free energy and certain operator dimensions, passing all checks against large-N results. We use two sided Pad\'e approximations with our epsilon expansion results to obtain estimates of various quantities in the physical dimension d=3. Finally, we provide evidence that the N=1 Gross-Neveu-Yukawa model which contains a 2-component Majorana fermion, and the N=2 Nambu-Jona-Lasinion-Yukawa model which contains a 2-component Dirac fermion, both have emergent supersymmetry.
*Advisors/Committee Members: Giombi, Simone (advisor).*

Subjects/Keywords: conformal field theory; epsilon expansion; large N expansion; O(N); Potts; supersymmetry

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APA (6^{th} Edition):

Fei, L. (2017). Conformal Field Theories in the Epsilon and 1/N Expansions . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp0144558g94m

Chicago Manual of Style (16^{th} Edition):

Fei, Lin. “Conformal Field Theories in the Epsilon and 1/N Expansions .” 2017. Doctoral Dissertation, Princeton University. Accessed September 19, 2019. http://arks.princeton.edu/ark:/88435/dsp0144558g94m.

MLA Handbook (7^{th} Edition):

Fei, Lin. “Conformal Field Theories in the Epsilon and 1/N Expansions .” 2017. Web. 19 Sep 2019.

Vancouver:

Fei L. Conformal Field Theories in the Epsilon and 1/N Expansions . [Internet] [Doctoral dissertation]. Princeton University; 2017. [cited 2019 Sep 19]. Available from: http://arks.princeton.edu/ark:/88435/dsp0144558g94m.

Council of Science Editors:

Fei L. Conformal Field Theories in the Epsilon and 1/N Expansions . [Doctoral Dissertation]. Princeton University; 2017. Available from: http://arks.princeton.edu/ark:/88435/dsp0144558g94m

Princeton University

2. Kirilin, Vladimir. Higher Spin Operators in Conformal Field Theories .

Degree: PhD, 2018, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01j6731654c

In this thesis we study higher spin operators in conformal field theories with weakly broken higher spin symmetry. Exact higher spin symmetry is known to be very constraining, containing the usual conformal group as a subgroup, and actually enforcing the theory to be free. Moreover, even in the presence of some weak, perturbative breaking of this symmetry, it still constrains the correlation functions.
In particular, it simplifies the calculation of anomalous dimensions of those currents to the lowest order in perturbation theory, reducing it to a two-point function of the non-conservation operator corresponding to the current. We apply this method to a variety of vector models, both bosonic and fermionic. Specifically, we reproduce some known results for Wilson-Fisher model in 4 − ε expansion, as well as the 1/N expansion of the model and use those to interpolate with good accuracy to d = 3 Ising model. We also get some new results for non-linear sigma model in 2 + ε expansion and cubic models in 6 − ε. We also apply this technique to fermionic models, the Gross-Neveu-Yukawa model in 4 − ε expansion and 1/N expansion. Further, we use a combination of direct Feynman diagram calculation and analytic bootstrap methods to calculate the anomalous dimension of some composite operators.
In the last chapter, we study vector models in d = 3 with a Chern-Simons interaction, which were an object of close study recently as a testing ground of a whole family of boson-fermion dualities. In particular, these dualities imply a matching of anomalous dimensions and three-point functions of higher spin currents between bosonic and fermionic theories under a certain mapping of the Chern- Simons coupling and the rank of the gauge group. We confirm those predictions using both the non-conservation operator formalism and a direct Feynman diagram calculation.
*Advisors/Committee Members: Giombi, Simone (advisor).*

Subjects/Keywords: CFT; Higher Spin Operators

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Kirilin, V. (2018). Higher Spin Operators in Conformal Field Theories . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01j6731654c

Chicago Manual of Style (16^{th} Edition):

Kirilin, Vladimir. “Higher Spin Operators in Conformal Field Theories .” 2018. Doctoral Dissertation, Princeton University. Accessed September 19, 2019. http://arks.princeton.edu/ark:/88435/dsp01j6731654c.

MLA Handbook (7^{th} Edition):

Kirilin, Vladimir. “Higher Spin Operators in Conformal Field Theories .” 2018. Web. 19 Sep 2019.

Vancouver:

Kirilin V. Higher Spin Operators in Conformal Field Theories . [Internet] [Doctoral dissertation]. Princeton University; 2018. [cited 2019 Sep 19]. Available from: http://arks.princeton.edu/ark:/88435/dsp01j6731654c.

Council of Science Editors:

Kirilin V. Higher Spin Operators in Conformal Field Theories . [Doctoral Dissertation]. Princeton University; 2018. Available from: http://arks.princeton.edu/ark:/88435/dsp01j6731654c