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• W2971307554 abstract "We show that 2 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mn>2</mml:mn></mml:math> d adjoint QCD, an SU(N) <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy=false form=prefix>(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy=false form=postfix>)</mml:mo></mml:mrow></mml:math> gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 2 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mn>2</mml:mn></mml:math> index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of N <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math> , are matched by spontaneous chiral symmetry breaking. We find that massless 2 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mn>2</mml:mn></mml:math> d adjoint QCD confines for N >2 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>N</mml:mi><mml:mo>></mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> , except for test charges of N <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math> -ality N/2 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>N</mml:mi><mml:mi>/</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:math> , which are deconfined. In other words, mathbb Z_N <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:msub><mml:mstyle mathvariant=double-struck><mml:mi>ℤ</mml:mi></mml:mstyle><mml:mi>N</mml:mi></mml:msub></mml:math> center symmetry is unbroken for odd N <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math> and spontaneously broken to mathbb Z_{N/2} <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:msub><mml:mstyle mathvariant=double-struck><mml:mi>ℤ</mml:mi></mml:mstyle><mml:mrow><mml:mi>N</mml:mi><mml:mi>/</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> for even N <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math> . All of these results are confirmed by explicit calculations on small mathbb{R}times S^1 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mstyle mathvariant=double-struck><mml:mi>ℝ</mml:mi></mml:mstyle><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mrow></mml:math> . We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when N <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math> is even. Furthermore, for most values of N <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math> , 2 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mn>2</mml:mn></mml:math> d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 8 <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mn>8</mml:mn></mml:math> . As a result, it fits into the classification of (1+1) <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mo stretchy=false form=prefix>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false form=postfix>)</mml:mo></mml:mrow></mml:math> d SPT phases of interacting Majorana fermions in an interesting way." @default.
• W2971307554 created "2019-09-05" @default.
• W2971307554 creator A5017673617 @default.
• W2971307554 creator A5053030256 @default.
• W2971307554 creator A5080722205 @default.
• W2971307554 creator A5089319910 @default.
• W2971307554 date "2020-05-05" @default.
• W2971307554 modified "2023-10-01" @default.
• W2971307554 title "Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD" @default.
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