- Peninei Halakha
During Shaĥarit and Minĥa of public fast days, we read the section of the Torah that describes how God forgave Israel after the sin of the Golden Calf (Sofrim 17:7, sa 566:1). This symbolizes that just as God forgave us for the sin of the Golden Calf and gave us a new set of Tablets, so will He forgive all of our sins and rebuild the Holy Temple, speedily in our days.
Most poskim maintain that we read the haftara beginning “Seek the Lord while He can be found” (Yeshayahu 55-56) at Minĥa, and all Ashkenazim follow this practice (Rema 566:1). However, most Sephardim do not customarily read a haftara. Nonetheless, a Sephardic man who is called up third to the Torah in a place where the custom is to read the haftara should read it and recite the accompanying berakhot (Yaskil Avdi 6:9).
These readings are read only if at least six people present are fasting. One who is not fasting should not be called up to the Torah. Bedi’avad, if one who is not fasting was called up to the Torah, and he is embarrassed to say that he is not fasting, he may go up to the Torah.
The Ashkenazic custom is to recite the Avinu Malkeinu prayer after the Amida of both Shaĥarit and Minĥa, while Sephardim do not recite it.
 mb 566:21 cites a dispute as to whether, be-di’avad, one who is not fasting may go up to the Torah if called, and concludes that if he is a Torah scholar and is worried about disgracing God’s name, he may go up. Torat Ha-mo’adim 4:5-6 writes that such a person should not go up to the Torah. Ĥatam Sofer, oĥ 157, however, maintains that one who is not fasting may go up to the Torah on mandatory fast days, and ahs 566:11 concurs. Therefore, it seems that anyone who is embarrassed may rely on these authorities and go up to the Torah.