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Topological quantum field theory
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<p>In <a href="/facts/Gauge_theory_(mathematics)/RPnPc4FG">gauge theory</a> and <a href="/facts/Mathematical_physics/sLKg8T1G">mathematical physics</a>, a topological quantum field theory (or topological field theory or TQFT) is a <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a> that computes <a href="/facts/Topological_invariant/vbJR18Sx">topological invariants</a>. </p><p>While TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, <a href="/facts/Knot_theory/mb7rtqVP">knot theory</a> and the theory of <a href="/facts/Four-manifold/XwVxwqnr">four-manifolds</a> in <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a>, and to the theory of <a href="/facts/Moduli_spaces/9sqrdpwR">moduli spaces</a> in <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>. <a href="/facts/Simon_Donaldson/zkQ5xq5u">Donaldson</a>, <a href="/facts/Vaughan_Jones/VMsx3l70">Jones</a>, <a href="/facts/Edward_Witten/lPUylPmj">Witten</a>, and <a href="/facts/Maxim_Kontsevich/7No1RaTQ">Kontsevich</a> have all won <a href="/facts/Fields_Medal/khFmkEnm">Fields Medals</a> for mathematical work related to topological field theory. </p><p>In <a href="/facts/Condensed_matter_physics/EBVI5nmL">condensed matter physics</a>, topological quantum field theories are the low-energy effective theories of <a href="/facts/Topological_order/EfEnKRSw">topologically ordered</a> states, such as <a href="/facts/Quantum_Hall_Effect/yK3zcCgu">fractional quantum Hall</a> states, <a href="/facts/String-net/djCBSlDm">string-net</a> condensed states, and other <a href="/facts/Strongly_correlated_quantum_spin_liquid/cUJx0mq8">strongly correlated quantum liquid</a> states. </p>