{"id":144,"date":"2005-01-29T11:47:05","date_gmt":"2005-01-29T15:47:05","guid":{"rendered":"http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=144"},"modified":"2005-01-29T11:47:05","modified_gmt":"2005-01-29T15:47:05","slug":"two-loop-superstring-amplitudes","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=144","title":{"rendered":"Two-Loop Superstring Amplitudes"},"content":{"rendered":"<p>Eric D&#8217;Hoker and D.H. Phong this past week finally posted two crucial papers with results from their work on two-loop superstring amplitudes.  The <A href=\"http:\/\/www.arxiv.org\/abs\/hep-th\/0501196\">first<\/A> one shows gauge slice independence of the two-loop N-point function, the <A href=\"http:\/\/www.arxiv.org\/abs\/hep-th\/0501197\">second<\/A> shows that, for N less than 3 and for low-order terms at N less than 4, there are no two-loop corrections to the low energy effective action.<\/p>\n<p>D&#8217;Hoker and Phong have been studying superstring amplitudes for nearly twenty years, and are justly proud of their recent results, which are a tour de force of careful calculation.  Over the years there have been many claims made about two-loop amplitudes, but until their work, no one had managed to really sort out the gauge dependence issues and write down gauge-independent amplitudes.  For some comments about some of the issues involved at genus 2 and higher, see postings by Jacques Distler <A href=\"http:\/\/golem.ph.utexas.edu\/~distler\/blog\/archives\/000472.html\">here<\/A>, <A href=\"http:\/\/golem.ph.utexas.edu\/~distler\/blog\/archives\/000474.html\">here<\/A>, and <A href=\"http:\/\/golem.ph.utexas.edu\/~distler\/blog\/archives\/000477.html\">here<\/A>.<\/p>\n<p>I don&#8217;t think D&#8217;Hoker and Phong will be coming out with complete results for genus 3 anytime soon, so the state of the art is that there is now a finite and well-defined version of the two-loop superstring amplitudes, with the problem of higher loops still open.  While claims abound about the finiteness of higher-loop amplitudes, before believing them one should first take a look at the tricky problems that D&#8217;Hoker and Phong had to overcome to get well-defined two-loop amplitudes.<\/p>\n<p>Update: Jacques Distler has a new <A href=\"http:\/\/golem.ph.utexas.edu\/~distler\/blog\/archives\/000504.html\">posting<\/A> about multi-loop amplitudes and potential problems with the Berkovits version of the superstring (he explains in more detail the possible problems with the BRST and picture-changing operators I mentioned).  For some mysterious reason Jacques neglects to refer to my posting or comments about this.  I encourage those commenters who seemed convinced I didn&#8217;t know what I was talking about to now take up their arguments with him.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Eric D&#8217;Hoker and D.H. Phong this past week finally posted two crucial papers with results from their work on two-loop superstring amplitudes. The first one shows gauge slice independence of the two-loop N-point function, the second shows that, for N &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=144\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-144","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/144","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=144"}],"version-history":[{"count":0,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/144\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=144"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=144"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=144"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}